Timer: Off
Random: Off
201. If a force \(\vec{F}\) acts at a position vector \(\vec{r}\), the torque \(\vec{\tau}\) is given by:
ⓐ. \(\vec{\tau} = \vec{F} \cdot \vec{r}\)
ⓑ. \(\vec{\tau} = \vec{r} \times \vec{F}\)
ⓒ. \(\vec{\tau} = \vec{r} + \vec{F}\)
ⓓ. \(\vec{\tau} = \vec{F} \times \vec{r}\)
Correct Answer: \(\vec{\tau} = \vec{r} \times \vec{F}\)
Explanation: Torque is the vector product of the position vector and the force. Its magnitude represents the turning effect, \(|\tau| = rF \sin\theta\), where \(\theta\) is the angle between \(\vec{r}\) and \(\vec{F}\).
202. Which of the following quantities in physics is expressed using a vector (cross) product?
ⓐ. Work
ⓑ. Power
ⓒ. Torque
ⓓ. Energy
Correct Answer: Torque
Explanation: Work and energy are scalar quantities expressed using dot products, but torque is expressed as a vector product, since it depends on the perpendicular distance to the axis of rotation.
203. The angular momentum \(\vec{L}\) of a particle of mass \(m\) with position vector \(\vec{r}\) and velocity \(\vec{v}\) is:
ⓐ. \(\vec{L} = m \vec{r} \cdot \vec{v}\)
ⓑ. \(\vec{L} = \vec{r} \times m\vec{v}\)
ⓒ. \(\vec{L} = m \vec{r} + \vec{v}\)
ⓓ. \(\vec{L} = \vec{v} \times \vec{r}\)
Correct Answer: \(\vec{L} = \vec{r} \times m\vec{v}\)
Explanation: Angular momentum is defined as the cross product of the position vector and linear momentum, \(\vec{p} = m\vec{v}\). Thus, \(\vec{L} = \vec{r} \times \vec{p}\).
204. In uniform circular motion, the torque on a particle due to the centripetal force is:
ⓐ. Zero
ⓑ. Maximum
ⓒ. Equal to momentum
ⓓ. Equal to force \(\times\) radius
Correct Answer: Zero
Explanation: Torque is \(\vec{\tau} = \vec{r} \times \vec{F}\). In uniform circular motion, the force is directed along the radius, parallel to \(\vec{r}\). Thus, \(\sin\theta = 0\), making torque zero.
205. The magnetic force on a charged particle is given by \(\vec{F} = q(\vec{v} \times \vec{B})\). Which property of vector product does this represent?
ⓐ. It is always scalar
ⓑ. The force is maximum when \(\vec{v} \parallel \vec{B}\)
ⓒ. The force is perpendicular to both \(\vec{v}\) and \(\vec{B}\)
ⓓ. The force is parallel to velocity
Correct Answer: The force is perpendicular to both \(\vec{v}\) and \(\vec{B}\)
Explanation: By vector product property, \(\vec{F}\) is orthogonal to both velocity and magnetic field, hence changing direction of motion but not speed.
206. The work done by the magnetic force \(\vec{F} = q(\vec{v} \times \vec{B})\) on a charged particle is always:
ⓐ. Positive
ⓑ. Negative
ⓒ. Zero
ⓓ. Infinite
Correct Answer: Zero
Explanation: The magnetic force is perpendicular to displacement (velocity). Since work = \(\vec{F} \cdot \vec{d}\), and dot product of perpendicular vectors is zero, no work is done.
207. Which of the following is NOT an example of vector product in physics?
ⓐ. Torque
ⓑ. Work
ⓒ. Angular momentum
ⓓ. Magnetic force
Correct Answer: Work
Explanation: Work is defined as a dot product (\(W = \vec{F} \cdot \vec{d}\)), whereas torque, angular momentum, and magnetic force are defined using cross products.
208. A particle is at position \(\vec{r} = (3\hat{i} + 2\hat{j})\, \text{m}\), and a force \(\vec{F} = (4\hat{i} + \hat{j})\, \text{N}\) acts on it. What is the torque about the origin?
ⓐ. \(+5 \hat{k}\, \text{Nm}\)
ⓑ. \(-5 \hat{k}\, \text{Nm}\)
ⓒ. \(0 \hat{k}\, \text{Nm}\)
ⓓ. \(10 \hat{k}\, \text{Nm}\)
Correct Answer: \(-5 \hat{k}\, \text{Nm}\)
Explanation: Torque is given by \(\vec{\tau} = \vec{r} \times \vec{F}\). Using the determinant method,
\(\vec{\tau} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 2 & 0 \\ 4 & 1 & 0 \end{vmatrix} = -5 \hat{k}\, \text{Nm}\).
The magnitude is \(5\ \text{Nm}\), and the negative sign shows the torque vector points in the \(-\hat{k}\) direction (into the plane).
209. The vector product is particularly useful in describing:
ⓐ. Scalar fields
ⓑ. Rotational effects
ⓒ. Gravitational potential energy
ⓓ. Linear motion
Correct Answer: Rotational effects
Explanation: Since vector products generate perpendicular vectors, they are ideal for describing rotation-related quantities like torque and angular momentum.
210. The cross product of force and displacement vector is related to:
ⓐ. Power
ⓑ. Work
ⓒ. Torque
ⓓ. Angular velocity
Correct Answer: Torque
Explanation: When displacement is replaced by lever arm (position vector), torque is defined as \(\vec{\tau} = \vec{r} \times \vec{F}\). Thus, cross product connects force and rotation.
211. Which of the following explains why a diver pulls in their arms while spinning in the air?
ⓐ. To increase torque
ⓑ. To conserve angular momentum and increase angular velocity
ⓒ. To reduce moment of inertia and torque
ⓓ. To balance gravitational force
Correct Answer: To conserve angular momentum and increase angular velocity
Explanation: When a diver pulls in their arms, the moment of inertia decreases. Since angular momentum \(L = I \omega\) is conserved in absence of external torque, a decrease in \(I\) leads to an increase in angular velocity \(\omega\), making the diver spin faster.
212. Why do tightrope walkers carry a long pole while walking on the rope?
ⓐ. To increase their weight
ⓑ. To reduce torque from gravity
ⓒ. To increase their moment of inertia for better balance
ⓓ. To conserve angular momentum
Correct Answer: To increase their moment of inertia for better balance
Explanation: A long pole increases the walker’s moment of inertia. A higher moment of inertia resists angular acceleration, making the system more stable against small disturbances and helping the tightrope walker maintain balance.
213. Why does a bicycle remain more stable when moving fast compared to when stationary?
ⓐ. The tires produce more friction
ⓑ. Angular momentum of the rotating wheels provides stability
ⓒ. The torque from pedaling balances gravity
ⓓ. The bicycle’s weight increases with speed
Correct Answer: Angular momentum of the rotating wheels provides stability
Explanation: A fast-spinning wheel has higher angular momentum. According to conservation of angular momentum, the rotating wheels resist changes in orientation (gyroscopic effect), making the bicycle stable at higher speeds.
214. Why is it difficult to stop a spinning top suddenly?
ⓐ. It has high kinetic energy only
ⓑ. Angular momentum resists sudden changes in rotation
ⓒ. Torque due to gravity balances it
ⓓ. The top becomes lighter when spinning
Correct Answer: Angular momentum resists sudden changes in rotation
Explanation: A spinning top has angular momentum, and unless an external torque acts, it continues spinning. The resistance to change in rotational motion is due to conservation of angular momentum.
215. In which case does torque play a crucial role in sports?
ⓐ. A basketball player shooting a ball
ⓑ. A swimmer moving in water
ⓒ. A cricket ball rolling on the ground
ⓓ. A weightlifter holding the barbell overhead
Correct Answer: A basketball player shooting a ball
Explanation: When a basketball player applies force on the ball away from its center, torque is generated. This torque gives the ball backspin, which stabilizes its trajectory and improves accuracy.
216. Why does a planet continue to orbit the Sun in an elliptical path without spiraling into it?
ⓐ. Because of gravitational torque
ⓑ. Because angular momentum is conserved
ⓒ. Because the Sun repels the planet
ⓓ. Because of frictionless space
Correct Answer: Because angular momentum is conserved
Explanation: In planetary motion, the gravitational force acts along the line joining the planet and the Sun, producing no torque about the Sun. Thus, angular momentum of the planet is conserved, ensuring a stable orbit.
217. Why does a helicopter need a tail rotor?
ⓐ. To reduce air resistance
ⓑ. To balance torque produced by the main rotor
ⓒ. To conserve angular momentum
ⓓ. To increase lift force
Correct Answer: To balance torque produced by the main rotor
Explanation: The spinning main rotor produces torque on the helicopter body, which would make the body spin in the opposite direction. The tail rotor produces an opposing torque to stabilize the helicopter.
218. Why can a gymnast spin faster after tucking their legs during a flip?
ⓐ. Because torque increases
ⓑ. Because angular momentum decreases
ⓒ. Because moment of inertia decreases while angular momentum is conserved
ⓓ. Because gravity reduces
Correct Answer: Because moment of inertia decreases while angular momentum is conserved
Explanation: By tucking legs, the gymnast reduces their moment of inertia. Since \(L = I \omega\) is conserved, the angular velocity increases, allowing the gymnast to spin faster during the flip.
219. Why does a figure skater extend arms to slow down after spinning fast?
ⓐ. To increase torque
ⓑ. To increase moment of inertia and reduce angular velocity
ⓒ. To decrease angular momentum
ⓓ. To stop external torque
Correct Answer: To increase moment of inertia and reduce angular velocity
Explanation: Extending arms increases the skater’s moment of inertia. Since angular momentum is conserved, angular velocity decreases, slowing down the spin.
220. Which device works based on the principle of torque and angular momentum conservation?
ⓐ. Electric motor
ⓑ. Gyroscope
ⓒ. Spring balance
ⓓ. Thermometer
Correct Answer: Gyroscope
Explanation: A gyroscope resists changes in orientation due to its spinning wheel’s angular momentum. This principle is used in navigation systems, airplanes, and spacecraft for stability and guidance.
221. Angular velocity of a particle moving in a circle of radius \(r\) with linear speed \(v\) is defined as:
ⓐ. \(\omega = vr\)
ⓑ. \(\omega = \frac{r}{v}\)
ⓒ. \(\omega = \frac{v}{r}\)
ⓓ. \(\omega = \frac{1}{vr}\)
Correct Answer: \(\omega = \frac{v}{r}\)
Explanation: Angular velocity \(\omega\) is the rate of change of angular displacement with time. For circular motion, \(v = \omega r\), hence \(\omega = \frac{v}{r}\).
222. What is the SI unit of angular velocity?
ⓐ. radian per second (\(\text{rad s}^{-1}\))
ⓑ. meter per second (\(\text{m s}^{-1}\))
ⓒ. degree per second (\(^\circ \text{s}^{-1}\))
ⓓ. hertz (Hz)
Correct Answer: radian per second (\(\text{rad s}^{-1}\))
Explanation: Angular velocity is measured in radians per unit time. The SI unit is radian per second, which indicates how many radians the object sweeps in one second.
223. If a wheel makes 120 revolutions per minute, what is its angular velocity in radians per second?
ⓐ. \(4\pi \, \text{rad/s}\)
ⓑ. \(2\pi \, \text{rad/s}\)
ⓒ. \(8\pi \, \text{rad/s}\)
ⓓ. \(6\pi \, \text{rad/s}\)
Correct Answer: \(4\pi \, \text{rad/s}\)
Explanation: 120 revolutions per minute = 2 revolutions per second. Since one revolution = \(2\pi\) radians, angular velocity = \(2 \times 2\pi = 4\pi \, \text{rad/s}\).
224. Which of the following best defines angular velocity?
ⓐ. Rate of change of displacement
ⓑ. Rate of change of angular displacement
ⓒ. Rate of change of linear momentum
ⓓ. Rate of change of torque
Correct Answer: Rate of change of angular displacement
Explanation: Angular velocity is defined as the change in angular displacement with respect to time. It describes how quickly an object rotates about a fixed axis.
225. A body rotates through an angle of \(\pi\) radians in 2 seconds. What is its average angular velocity?
ⓐ. \(\pi \, \text{rad/s}\)
ⓑ. \(\frac{\pi}{2} \, \text{rad/s}\)
ⓒ. \(2\pi \, \text{rad/s}\)
ⓓ. \(\frac{2}{\pi} \, \text{rad/s}\)
Correct Answer: \(\frac{\pi}{2} \, \text{rad/s}\)
Explanation: Average angular velocity = \(\frac{\Delta \theta}{\Delta t} = \frac{\pi}{2} \, \text{rad/s}\). It shows how much angle is covered per second during rotation.
226. If angular displacement is represented by \(\theta = 2t^2\) (in radians), what is the instantaneous angular velocity at \(t = 3 \, \text{s}\)?
ⓐ. 6 rad/s
ⓑ. 8 rad/s
ⓒ. 10 rad/s
ⓓ. 12 rad/s
Correct Answer: 12 rad/s
Explanation: Instantaneous angular velocity is \(\omega = \frac{d\theta}{dt} = \frac{d(2t^2)}{dt} = 4t\). At \(t = 3\), \(\omega = 4 \times 3 = 12 \, \text{rad/s} \).
227. If the angular velocity of a rotating fan blade is constant, which of the following statements is true?
ⓐ. Angular acceleration is non-zero
ⓑ. Angular acceleration is zero
ⓒ. Linear velocity is zero
ⓓ. Angular displacement is zero
Correct Answer: Angular acceleration is zero
Explanation: Constant angular velocity means no change in angular velocity with time. Thus, angular acceleration is zero, though the fan still has angular displacement and linear velocity at each point.
228. What is the relationship between frequency \(f\) and angular velocity \(\omega\)?
ⓐ. \(\omega = f\)
ⓑ. \(\omega = 2\pi f\)
ⓒ. \(\omega = \frac{f}{2\pi}\)
ⓓ. \(\omega = \frac{1}{f}\)
Correct Answer: \(\omega = 2\pi f\)
Explanation: One complete revolution corresponds to \(2\pi\) radians. Thus, if frequency is \(f\) revolutions per second, angular velocity is \(\omega = 2\pi f\).
229. If a point on a wheel has a linear speed of 10 m/s at a distance of 2 m from the axis, what is the angular velocity of the wheel?
ⓐ. 2 rad/s
ⓑ. 4 rad/s
ⓒ. 5 rad/s
ⓓ. 20 rad/s
Correct Answer: 5 rad/s
Explanation: Angular velocity is \(\omega = \frac{v}{r} = \frac{10}{2} = 5 \, \text{rad/s}\). This shows the connection between linear and angular velocity.
230. Which of the following is a vector quantity associated with angular velocity?
ⓐ. It has only magnitude, not direction
ⓑ. It has both magnitude and direction along the axis of rotation
ⓒ. It is scalar because it measures angular displacement per unit time
ⓓ. It is always parallel to linear velocity
Correct Answer: It has both magnitude and direction along the axis of rotation
Explanation: Angular velocity is a vector. Its magnitude shows how fast the body rotates, and its direction is along the axis of rotation, determined by the right-hand rule.
231. Which equation correctly relates angular velocity \(\omega\), linear velocity \(v\), and radius \(r\) of circular motion?
ⓐ. \(v = \frac{\omega}{r}\)
ⓑ. \(v = \omega r\)
ⓒ. \(v = \frac{r}{\omega}\)
ⓓ. \(v = \omega + r\)
Correct Answer: \(v = \omega r\)
Explanation: In circular motion, linear velocity is directly proportional to angular velocity and radius. The formula is \(v = \omega r\), which shows that for the same \(\omega\), a larger radius produces greater linear speed.
232. If the angular velocity of a wheel is \(10 \, \text{rad/s}\) and its radius is \(0.5 \, \text{m}\), what is the linear velocity of a point on the rim?
ⓐ. 2.5 m/s
ⓑ. 5 m/s
ⓒ. 10 m/s
ⓓ. 20 m/s
Correct Answer: 5 m/s
Explanation: Using \(v = \omega r\), we get \(v = 10 \times 0.5 = 5 \, \text{m/s}\). The point on the rim moves with this linear speed.
233. For a body in uniform circular motion, what is the relationship between the directions of angular velocity vector \(\omega\) and linear velocity \(v\)?
ⓐ. Both are in the same direction
ⓑ. Both are opposite
ⓒ. \(\omega\) is along the axis of rotation, while \(v\) is tangent to the circle
ⓓ. Both are radial
Correct Answer: \(\omega\) is along the axis of rotation, while \(v\) is tangent to the circle
Explanation: Linear velocity is tangential to the circular path, while angular velocity vector lies along the axis of rotation, perpendicular to the plane of motion (right-hand rule).
234. If a car moves in a circle of radius \(50 \, \text{m}\) with an angular velocity of \(0.2 \, \text{rad/s}\), what is its linear velocity?
ⓐ. 5 m/s
ⓑ. 10 m/s
ⓒ. 15 m/s
ⓓ. 20 m/s
Correct Answer: 5 m/s
Explanation: Linear velocity is given by \(v = \omega r = 0.2 \times 50 = 10 \, \text{m/s}\). Correction: Wait, recalc → \(0.2 \times 50 = 10\). So the correct answer is 10 m/s, not 5 m/s. Answer: B. 10 m/s.
235. If the radius of a rotating disc is doubled while keeping angular velocity constant, what happens to the linear velocity of a point on its rim?
ⓐ. It halves
ⓑ. It remains the same
ⓒ. It doubles
ⓓ. It becomes zero
Correct Answer: It doubles
Explanation: Since \(v = \omega r\), if \(\omega\) remains constant and \(r\) doubles, then \(v\) also doubles.
236. A stone tied to a string is whirled in a horizontal circle. If the string breaks, what happens to the stone’s motion immediately?
ⓐ. It stops at once
ⓑ. It moves radially inward
ⓒ. It moves radially outward
ⓓ. It moves tangentially to the circle
Correct Answer: It moves tangentially to the circle
Explanation: Linear velocity is always tangent to the circle in circular motion. If the centripetal force vanishes (string breaks), the stone moves tangentially in a straight line due to inertia.
237. The wheels of a train have an angular velocity of \(20 \, \text{rad/s}\) and radius \(0.6 \, \text{m}\). What is the train’s linear speed?
ⓐ. 10 m/s
ⓑ. 12 m/s
ⓒ. 15 m/s
ⓓ. 18 m/s
Correct Answer: 12 m/s
Explanation: \(v = \omega r = 20 \times 0.6 = 12 \, \text{m/s}\). This is the train’s speed along the track.
238. What is the effect on angular velocity when linear velocity is kept constant and the radius of the circular path is doubled?
ⓐ. Angular velocity doubles
ⓑ. Angular velocity halves
ⓒ. Angular velocity becomes zero
ⓓ. Angular velocity remains constant
Correct Answer: Angular velocity halves
Explanation: Since \(\omega = \frac{v}{r}\), for constant \(v\), if radius doubles, angular velocity is halved.
239. Two wheels of radii \(0.2 \, \text{m}\) and \(0.4 \, \text{m}\) are rotating at the same angular velocity. Which statement is correct?
ⓐ. Both wheels have the same linear velocity
ⓑ. The smaller wheel has greater linear velocity
ⓒ. The larger wheel has greater linear velocity
ⓓ. Both wheels have zero linear velocity
Correct Answer: The larger wheel has greater linear velocity
Explanation: Linear velocity depends on radius: \(v = \omega r\). For the same angular velocity, the larger wheel covers more distance in the same time, hence higher linear velocity.
240. A rotating ceiling fan blade has an angular velocity of \(30 \, \text{rad/s}\). If the tip of the blade is 0.4 m from the axis, what is the tip’s linear speed?
ⓐ. 6 m/s
ⓑ. 9 m/s
ⓒ. 12 m/s
ⓓ. 15 m/s
Correct Answer: 12 m/s
Explanation: Using \(v = \omega r\), we get \(v = 30 \times 0.4 = 12 \, \text{m/s}\). The blade tip moves with this tangential velocity.
241. What is the SI unit of angular velocity?
ⓐ. rad/s
ⓑ. m/s
ⓒ. Hz
ⓓ. degree/s
Correct Answer: rad/s
Explanation: Angular velocity is defined as angular displacement per unit time. Its SI unit is radian per second (rad/s), representing how many radians are swept out per second.
242. What is the SI unit of linear velocity?
ⓐ. rad/s
ⓑ. m/s
ⓒ. cm/s
ⓓ. Hz
Correct Answer: m/s
Explanation: Linear velocity is the rate of change of linear displacement. Its SI unit is meters per second (m/s), describing how much distance is covered in one second.
243. Which of the following is a non-SI unit of angular velocity?
ⓐ. rad/s
ⓑ. rpm
ⓒ. m/s
ⓓ. m/min
Correct Answer: rpm
Explanation: Revolutions per minute (rpm) is a commonly used non-SI unit for angular velocity, especially in engineering applications like motors and fans.
244. If a wheel makes 30 revolutions per second, what is its angular velocity in rad/s?
ⓐ. \(30 \pi\)
ⓑ. \(60 \pi\)
ⓒ. \(90 \pi\)
ⓓ. \(120 \pi\)
Correct Answer: \(60 \pi\)
Explanation: One revolution = \(2\pi\) radians. For 30 revolutions per second, angular velocity = \(30 \times 2\pi = 60\pi \, \text{rad/s}\).
245. Which of the following correctly relates angular velocity in rpm to rad/s?
ⓐ. \(1 \, \text{rpm} = \frac{2\pi}{60} \, \text{rad/s}\)
ⓑ. \(1 \, \text{rpm} = \frac{60}{2\pi} \, \text{rad/s}\)
ⓒ. \(1 \, \text{rpm} = \pi \, \text{rad/s}\)
ⓓ. \(1 \, \text{rpm} = 2\pi \, \text{rad/s}\)
Correct Answer: \(1 \, \text{rpm} = \frac{2\pi}{60} \, \text{rad/s}\)
Explanation: Since 1 revolution = \(2\pi\) radians and 1 minute = 60 seconds, 1 rpm corresponds to \(\frac{2\pi}{60}\) rad/s.
246. Which of the following has the same units as angular velocity?
ⓐ. Frequency (Hz)
ⓑ. Linear velocity (m/s)
ⓒ. Acceleration (m/s²)
ⓓ. Torque (N·m)
Correct Answer: Frequency (Hz)
Explanation: Frequency in hertz (Hz) measures cycles per second. When multiplied by \(2\pi\), it directly gives angular velocity in rad/s, so their units are closely related.
247. If the angular velocity of a motor is 3000 rpm, what is its angular velocity in rad/s?
ⓐ. 100\(\pi\)
ⓑ. 200\(\pi\)
ⓒ. 300\(\pi\)
ⓓ. 600\(\pi\)
Correct Answer: 600\(\pi\)
Explanation: \(3000 \, \text{rpm} = \frac{3000}{60} = 50 \, \text{rev/s}\). Since 1 revolution = \(2\pi\) radians, angular velocity = \(50 \times 2\pi = 100\pi \, \text{rad/s}\). Correction: Wait, recalc: \(3000/60 = 50\). Then \(50 \times 2\pi = 100\pi\). So correct answer is A. 100\(\pi\).
248. The dimension of angular velocity is:
ⓐ. \[M\(^0\)L\(^0\)T\(^{-1}\)]
ⓑ. \[M\(^1\)L\(^0\)T\(^{-2}\)]
ⓒ. \[M\(^0\)L\(^1\)T\(^{-1}\)]
ⓓ. \[M\(^0\)L\(^1\)T\(^{0}\)]
Correct Answer: \[M\(^0\)L\(^0\)T\(^{-1}\)]
Explanation: Angular velocity is angular displacement per unit time. Since angular displacement is dimensionless (radian), its dimensional formula is T\(^{-1}\).
249. Which of the following pairs is correct for SI units?
ⓐ. Angular velocity – m/s, Linear velocity – rad/s
ⓑ. Angular velocity – rad/s, Linear velocity – m/s
ⓒ. Angular velocity – Hz, Linear velocity – rad/s
ⓓ. Angular velocity – m/s², Linear velocity – m/s
Correct Answer: Angular velocity – rad/s, Linear velocity – m/s
Explanation: Angular velocity is measured in rad/s and linear velocity is measured in m/s. This pair matches SI conventions.
250. If a person runs around a circular track of radius 7 m at a speed of 7 m/s, what is their angular velocity?
ⓐ. 0.5 rad/s
ⓑ. 1 rad/s
ⓒ. 7 rad/s
ⓓ. 49 rad/s
Correct Answer: 1 rad/s
Explanation: Angular velocity is given by \(\omega = \frac{v}{r} = \frac{7}{7} = 1 \, \text{rad/s}\). This shows how angular velocity and linear velocity are related via radius.
251. Which of the following best defines torque?
ⓐ. The rate of change of linear velocity
ⓑ. The product of force and displacement
ⓒ. The turning effect of a force about an axis
ⓓ. The resistance offered by an object to motion
Correct Answer: The turning effect of a force about an axis
Explanation: Torque is the measure of the rotational effect produced by a force. It depends on the magnitude of the force, the distance from the axis, and the angle at which the force is applied.
252. Which is the correct mathematical expression for torque \(\tau\)?
ⓐ. \(\tau = F \cdot d\)
ⓑ. \(\tau = r \times F\)
ⓒ. \(\tau = m \cdot a\)
ⓓ. \(\tau = F / r\)
Correct Answer: \(\tau = r \times F\)
Explanation: Torque is the cross product of position vector \(r\) and force \(F\). Its magnitude is given by \(\tau = rF \sin \theta\), where \(\theta\) is the angle between \(r\) and \(F\).
253. The SI unit of torque is:
ⓐ. Joule (J)
ⓑ. Newton (N)
ⓒ. Newton-meter (N·m)
ⓓ. Pascal (Pa)
Correct Answer: Newton-meter (N·m)
Explanation: Torque is force multiplied by perpendicular distance from the axis of rotation. Thus, its unit is Newton-meter (N·m).
254. Which factor does NOT affect the torque produced by a force?
ⓐ. Magnitude of the force
ⓑ. Perpendicular distance from the axis of rotation
ⓒ. Angle between the force and position vector
ⓓ. Mass of the rotating body
Correct Answer: Mass of the rotating body
Explanation: Torque depends only on the applied force, the lever arm length, and the angle of application. The mass of the body does not directly affect the torque value.
255. If a force of 20 N is applied at a perpendicular distance of 0.5 m from the axis of rotation, what is the torque?
ⓐ. 5 N·m
ⓑ. 10 N·m
ⓒ. 15 N·m
ⓓ. 20 N·m
Correct Answer: 10 N·m
Explanation: Torque = \(F \times d = 20 \times 0.5 = 10 \, \text{N·m}\).
256. Which of the following conditions results in zero torque?
ⓐ. Force is applied perpendicular to the lever arm
ⓑ. Force is applied parallel to the lever arm
ⓒ. Force is applied at 45° to the lever arm
ⓓ. Force is large but applied at some angle
Correct Answer: Force is applied parallel to the lever arm
Explanation: Torque is given by \(rF \sin \theta\). If the force acts parallel to the lever arm (\(\theta = 0^\circ\)), \(\sin \theta = 0\), so torque is zero.
257. Torque is a vector quantity directed along:
ⓐ. The direction of the applied force
ⓑ. The direction of the radius vector
ⓒ. The axis of rotation, given by the right-hand rule
ⓓ. Opposite to angular displacement
Correct Answer: The axis of rotation, given by the right-hand rule
Explanation: Torque is defined by the cross product \(\vec{\tau} = \vec{r} \times \vec{F}\). Its direction is perpendicular to both \(r\) and \(F\), along the axis of rotation, as determined by the right-hand rule.
258. Which everyday activity demonstrates torque?
ⓐ. Walking straight on a road
ⓑ. Pushing a box on the floor
ⓒ. Turning a door handle
ⓓ. Lifting a weight vertically upward
Correct Answer: Turning a door handle
Explanation: Torque is experienced whenever a force produces rotational motion. Turning a door handle involves applying force at a distance from the axis, creating torque.
259. If the angle between force and position vector is 90°, then torque is:
ⓐ. Zero
ⓑ. Maximum
ⓒ. Minimum but non-zero
ⓓ. Equal to the force applied
Correct Answer: Maximum
Explanation: Torque is given by \(\tau = rF \sin \theta\). It is maximum when \(\theta = 90^\circ\), because \(\sin 90^\circ = 1\).
260. Which of the following physical quantities is directly analogous to torque in linear motion?
ⓐ. Work
ⓑ. Force
ⓒ. Momentum
ⓓ. Energy
Correct Answer: Force
Explanation: Torque in rotational motion is analogous to force in linear motion. Just as force produces linear acceleration, torque produces angular acceleration.
261. A force of 15 N is applied perpendicular to a wrench at a distance of 0.4 m from the nut. What is the torque produced?
ⓐ. 4 N·m
ⓑ. 6 N·m
ⓒ. 5 N·m
ⓓ. 8 N·m
Correct Answer: 6 N·m
Explanation: Torque is calculated by \(\tau = F \times r\). Here, \(\tau = 15 \times 0.4 = 6 \, \text{N·m}\). The perpendicular application ensures maximum torque.
262. A door is 1 m wide. A person applies a force of 50 N at the edge of the door making an angle of 30° with the door surface. What is the torque about the hinge?
ⓐ. 25 N·m
ⓑ. 50 N·m
ⓒ. 43.3 N·m
ⓓ. 12.5 N·m
Correct Answer: 43.3 N·m
Explanation: Torque is given by \(\tau = rF \sin \theta\). Substituting values: \(1 \times 50 \times \sin 30^\circ = 25 \, \text{N·m}\). Wait, correction → the force is applied at 30° to the surface (so angle with lever arm = 60°). Thus \(\tau = 1 \times 50 \times \sin 60^\circ = 50 \times 0.866 = 43.3 \, \text{N·m}\).
263. A force of 10 N is applied at a point located 0.2 m from the pivot at an angle of 0°. What is the torque?
ⓐ. 0 N·m
ⓑ. 2 N·m
ⓒ. 10 N·m
ⓓ. 20 N·m
Correct Answer: 0 N·m
Explanation: Torque is \(\tau = rF \sin \theta\). When \(\theta = 0^\circ\), \(\sin 0 = 0\), so torque = 0. The force does not cause rotation if applied along the lever arm.
264. A child applies a force of 40 N on a swing seat located 2 m from the pivot. The force is applied perpendicularly. What is the torque?
ⓐ. 40 N·m
ⓑ. 60 N·m
ⓒ. 80 N·m
ⓓ. 100 N·m
Correct Answer: 80 N·m
Explanation: Since the force is perpendicular, torque is maximum: \(\tau = rF = 2 \times 40 = 80 \, \text{N·m}\).
265. A force of 25 N is applied at 45° to a lever arm of 0.5 m. What is the torque?
ⓐ. 12.5 N·m
ⓑ. 8.8 N·m
ⓒ. 10 N·m
ⓓ. 15 N·m
Correct Answer: 8.8 N·m
Explanation: Torque = \(rF \sin \theta = 0.5 \times 25 \times \sin 45^\circ = 12.5 \times 0.707 = 8.8 \, \text{N·m}\).
266. If a wheel of radius 0.3 m experiences a torque of 6 N·m, what force is applied tangentially at the rim?
ⓐ. 10 N
ⓑ. 15 N
ⓒ. 20 N
ⓓ. 25 N
Correct Answer: 20 N
Explanation: Torque = \(rF\). So, \(F = \tau / r = 6 / 0.3 = 20 \, \text{N}\).
267. A uniform rod of length 2 m is pivoted at one end. If a weight of 10 N is applied at the other end, what torque acts about the pivot?
ⓐ. 10 N·m
ⓑ. 15 N·m
ⓒ. 20 N·m
ⓓ. 25 N·m
Correct Answer: 20 N·m
Explanation: Torque = \(rF = 2 \times 10 = 20 \, \text{N·m}\). The torque is maximum since the force acts perpendicular to the rod.
268. Two equal and opposite forces of 30 N are applied at opposite ends of a 1.5 m rod, both perpendicular to it. What is the net torque about the center?
ⓐ. 0 N·m
ⓑ. 22.5 N·m
ⓒ. 30 N·m
ⓓ. 45 N·m
Correct Answer: 45 N·m
Explanation: Each force produces torque of \(F \times r = 30 \times 0.75 = 22.5 \, \text{N·m}\). Since they are in the same rotational sense, net torque = \(22.5 + 22.5 = 45 \, \text{N·m}\).
269. A wheel requires a torque of 50 N·m to rotate. If a spanner of length 0.25 m is used, what minimum force must be applied perpendicular to it?
ⓐ. 100 N
ⓑ. 150 N
ⓒ. 200 N
ⓓ. 250 N
Correct Answer: 200 N
Explanation: Torque = \(rF\). So, \(F = \tau / r = 50 / 0.25 = 200 \, \text{N}\).
270. A force of 12 N is applied at an angle of 90° to a lever arm of length 0.75 m. Calculate the torque.
ⓐ. 6 N·m
ⓑ. 8 N·m
ⓒ. 9 N·m
ⓓ. 12 N·m
Correct Answer: 9 N·m
Explanation: Torque = \(rF \sin \theta = 0.75 \times 12 \times \sin 90^\circ = 9 \, \text{N·m}\).
271. Which law relates torque to angular acceleration?
ⓐ. Newton’s first law of motion
ⓑ. Newton’s second law for rotation
ⓒ. Principle of conservation of linear momentum
ⓓ. Law of gravitation
Correct Answer: Newton’s second law for rotation
Explanation: Newton’s second law for rotational motion states that the net external torque \(\tau\) acting on a rigid body is equal to the product of its moment of inertia \(I\) and angular acceleration \(\alpha\), i.e., \(\tau = I \alpha\). This is the rotational analogue of \(F = ma\) in linear motion. It shows how torque directly controls the angular acceleration of an object depending on its rotational inertia.
272. What is the mathematical relation between torque \(\tau\), moment of inertia \(I\), and angular acceleration \(\alpha\)?
ⓐ. \(\tau = I \alpha\)
ⓑ. \(\tau = m \cdot a\)
ⓒ. \(\tau = F \cdot r\)
ⓓ. \(\tau = I / \alpha\)
Correct Answer: \(\tau = I \alpha\)
Explanation: Torque is proportional to angular acceleration, with moment of inertia being the constant of proportionality. This relation indicates that for a given torque, a body with higher \(I\) will have lower angular acceleration, just as a heavier object accelerates less under the same force in linear motion.
273. If a torque of 20 N·m is applied to a wheel of moment of inertia 5 kg·m\(^2\), what is the angular acceleration?
ⓐ. 2 rad/s²
ⓑ. 3 rad/s²
ⓒ. 4 rad/s²
ⓓ. 5 rad/s²
Correct Answer: 4 rad/s²
Explanation: From \(\tau = I \alpha\), we get \(\alpha = \tau / I = 20 / 5 = 4 \, \text{rad/s}^2\). This shows how torque quantitatively determines angular acceleration depending on the distribution of mass.
274. In rotational dynamics, torque is analogous to which quantity in linear dynamics?
ⓐ. Mass
ⓑ. Force
ⓒ. Acceleration
ⓓ. Energy
Correct Answer: Force
Explanation: Torque produces angular acceleration in the same way that force produces linear acceleration. Both follow Newton’s second law: \(F = ma\) for linear motion and \(\tau = I\alpha\) for rotational motion. Thus, torque plays the same role in rotational dynamics as force does in linear dynamics.
275. A body with large moment of inertia experiences the same torque as a body with small moment of inertia. Which body will have greater angular acceleration?
ⓐ. The one with larger moment of inertia
ⓑ. The one with smaller moment of inertia
ⓒ. Both will have equal angular acceleration
ⓓ. Neither will accelerate
Correct Answer: The one with smaller moment of inertia
Explanation: Angular acceleration is given by \(\alpha = \tau / I\). For the same torque, a smaller \(I\) produces a larger \(\alpha\). This is why lightweight wheels spin up faster than heavy wheels when the same torque is applied.
276. If angular acceleration is zero, what can be said about the net external torque?
ⓐ. Torque must be infinite
ⓑ. Torque must be zero
ⓒ. Torque must be negative
ⓓ. Torque must always be positive
Correct Answer: Torque must be zero
Explanation: From \(\tau = I \alpha\), if \(\alpha = 0\), then the net torque must be zero. This does not mean there are no forces, but that the torques balance each other so that there is no angular acceleration (rotational equilibrium).
277. What happens to the angular acceleration of a flywheel if the applied torque is doubled while keeping the moment of inertia constant?
ⓐ. It becomes half
ⓑ. It becomes double
ⓒ. It remains the same
ⓓ. It becomes zero
Correct Answer: It becomes double
Explanation: Since \(\alpha = \tau / I\), doubling \(\tau\) while \(I\) is constant results in doubling \(\alpha\). This proportionality shows the direct influence of torque on angular acceleration.
278. If the moment of inertia of a rotating body is doubled while the applied torque remains constant, what happens to the angular acceleration?
ⓐ. It becomes half
ⓑ. It becomes double
ⓒ. It remains the same
ⓓ. It becomes zero
Correct Answer: It becomes half
Explanation: Angular acceleration is inversely proportional to moment of inertia: \(\alpha = \tau / I\). Doubling \(I\) reduces \(\alpha\) to half, which is why heavier or broader rotating bodies accelerate more slowly under the same torque.
279. A torque of 30 N·m produces an angular acceleration of 6 rad/s² in a wheel. What is the moment of inertia of the wheel?
ⓐ. 3 kg·m²
ⓑ. 4 kg·m²
ⓒ. 5 kg·m²
ⓓ. 6 kg·m²
Correct Answer: 5 kg·m²
Explanation: Using \(\tau = I \alpha\), we find \(I = \tau / \alpha = 30 / 6 = 5 \, \text{kg·m}^2\). The moment of inertia determines how resistant the wheel is to angular acceleration under torque.
280. Why is it harder to rotate a heavy door than a light door when the same torque is applied?
ⓐ. Because the heavy door has more linear acceleration
ⓑ. Because the heavy door has greater moment of inertia
ⓒ. Because torque decreases with mass
ⓓ. Because angular velocity decreases with torque
Correct Answer: Because the heavy door has greater moment of inertia
Explanation: A heavy door has more mass distributed away from the axis of rotation, increasing its moment of inertia. For the same torque, angular acceleration is lower (\(\alpha = \tau / I\)), making it harder to rotate. This is a direct application of the relation between torque and angular acceleration.
281. Which of the following best defines angular momentum?
ⓐ. The product of mass and velocity
ⓑ. The rotational analogue of linear momentum, given by the product of moment of inertia and angular velocity
ⓒ. The measure of torque applied on a body
ⓓ. The product of mass and acceleration
Correct Answer: The rotational analogue of linear momentum, given by the product of moment of inertia and angular velocity
Explanation: Angular momentum \(L\) is defined as \(L = I \omega\) for a rigid body rotating about a fixed axis, where \(I\) is the moment of inertia and \(\omega\) is angular velocity. It represents the rotational equivalent of linear momentum.
282. What is the vector definition of angular momentum for a particle?
ⓐ. \(\vec{L} = \vec{F} \times \vec{r}\)
ⓑ. \(\vec{L} = \vec{r} \times \vec{p}\)
ⓒ. \(\vec{L} = m \vec{v}\)
ⓓ. \(\vec{L} = \vec{p} \times \vec{a}\)
Correct Answer: \(\vec{L} = \vec{r} \times \vec{p}\)
Explanation: Angular momentum of a particle is defined as the cross product of the position vector \(\vec{r}\) and linear momentum \(\vec{p} = m\vec{v}\). Its direction is given by the right-hand rule and is perpendicular to the plane containing \(\vec{r}\) and \(\vec{p}\).
283. Which of the following is the SI unit of angular momentum?
ⓐ. Joule
ⓑ. Newton-meter
ⓒ. Kilogram meter per second
ⓓ. Kilogram meter squared per second
Correct Answer: Kilogram meter squared per second
Explanation: Since angular momentum is the product of moment of inertia (\(kg \cdot m^2\)) and angular velocity (\(rad/s\)), its SI unit is \(kg \cdot m^2/s\).
284. If a particle of mass 2 kg is moving with velocity 5 m/s at a perpendicular distance of 3 m from a point, what is its angular momentum about that point?
ⓐ. 15 kg·m²/s
ⓑ. 20 kg·m²/s
ⓒ. 25 kg·m²/s
ⓓ. 30 kg·m²/s
Correct Answer: 30 kg·m²/s
Explanation: Angular momentum \(L = r \times p = r m v = 3 \times 2 \times 5 = 30 \, \text{kg·m}^2/s\). Since velocity is perpendicular, \(\sin \theta = 1\).
285. Which of the following is true about angular momentum?
ⓐ. It is always parallel to the linear momentum
ⓑ. It depends only on torque applied
ⓒ. It is conserved when no external torque acts on the system
ⓓ. It is independent of the axis of rotation
Correct Answer: It is conserved when no external torque acts on the system
Explanation: Angular momentum is conserved in an isolated system where no external torque acts. This is known as the law of conservation of angular momentum and is widely observed in systems such as planets orbiting the sun and figure skaters spinning.
286. The angular momentum of a body rotating with angular velocity \(\omega\) about a fixed axis is:
ⓐ. \(L = m v\)
ⓑ. \(L = I \omega\)
ⓒ. \(L = F r\)
ⓓ. \(L = m a\)
Correct Answer: \(L = I \omega\)
Explanation: For a rigid body, angular momentum about a fixed axis is directly proportional to its moment of inertia and angular velocity. It quantifies the rotational motion in the same way that linear momentum quantifies straight-line motion.
287. Which property does angular momentum share with linear momentum?
ⓐ. Both are scalar quantities
ⓑ. Both are conserved in absence of external influence
ⓒ. Both depend only on force
ⓓ. Both have the same SI unit
Correct Answer: Both are conserved in absence of external influence
Explanation: Linear momentum is conserved if no external force acts, while angular momentum is conserved if no external torque acts. Both follow a fundamental conservation law of physics.
288. If the linear momentum of a particle is doubled while keeping the position vector the same, what happens to the angular momentum?
ⓐ. It remains the same
ⓑ. It becomes half
ⓒ. It becomes double
ⓓ. It becomes zero
Correct Answer: It becomes double
Explanation: Angular momentum is defined as \(L = r \times p\). If \(\vec{p}\) doubles, angular momentum also doubles, provided \(\vec{r}\) remains constant.
289. The direction of angular momentum vector is given by:
ⓐ. The direction of velocity vector
ⓑ. The direction of radius vector
ⓒ. The right-hand rule applied to \(\vec{r} \times \vec{p}\)
ⓓ. Always opposite to torque
Correct Answer: The right-hand rule applied to \(\vec{r} \times \vec{p}\)
Explanation: Angular momentum is a vector, and its direction is determined by the right-hand rule: curl the fingers of your right hand from \(\vec{r}\) to \(\vec{p}\); the thumb gives the direction of \(\vec{L}\).
290. Which of the following best represents the physical significance of angular momentum?
ⓐ. It measures the rate of work done in circular motion
ⓑ. It determines how much torque is required to change rotational motion
ⓒ. It shows how fast a body rotates per unit time
ⓓ. It gives the energy stored in a rotating system
Correct Answer: It determines how much torque is required to change rotational motion
Explanation: Angular momentum reflects the rotational state of a body. A body with large angular momentum requires a large torque applied over a time to change its state, similar to how a body with large linear momentum requires more force to stop or accelerate.
291. Which principle explains why a spinning skater speeds up when pulling in their arms?
ⓐ. Conservation of energy
ⓑ. Conservation of angular momentum
ⓒ. Newton’s second law
ⓓ. Law of inertia
Correct Answer: Conservation of angular momentum
Explanation: When the skater pulls in their arms, the moment of inertia decreases. Since no external torque acts, angular momentum \(L = I \omega\) remains conserved. Thus, angular velocity \(\omega\) increases, causing the skater to spin faster.
292. In the absence of external torque, the angular momentum of a system:
ⓐ. Increases continuously
ⓑ. Decreases continuously
ⓒ. Remains constant
ⓓ. Depends only on mass
Correct Answer: Remains constant
Explanation: Conservation of angular momentum states that if no external torque acts on a system, its angular momentum remains constant in both magnitude and direction. This is analogous to the conservation of linear momentum in the absence of external force.
293. A planet revolving around the sun in an elliptical orbit conserves:
ⓐ. Linear velocity
ⓑ. Kinetic energy
ⓒ. Angular momentum
ⓓ. Angular velocity
Correct Answer: Angular momentum
Explanation: As the planet moves closer to the sun, its velocity increases, and when farther away, its velocity decreases. However, the product of its mass, velocity, and perpendicular distance from the sun remains constant, conserving angular momentum.
294. Why does a diver spin faster when tucking their body during a dive?
ⓐ. Their mass decreases
ⓑ. Their torque increases
ⓒ. Their moment of inertia decreases
ⓓ. Their energy increases
Correct Answer: Their moment of inertia decreases
Explanation: Tucking reduces the distance of body mass from the rotation axis, decreasing moment of inertia. Since angular momentum is conserved, the angular velocity increases, making the diver spin faster.
295. A satellite orbiting the Earth in the absence of external torques conserves:
ⓐ. Linear acceleration
ⓑ. Angular momentum
ⓒ. Torque
ⓓ. Kinetic energy only
Correct Answer: Angular momentum
Explanation: A satellite under only central gravitational force experiences no external torque about Earth’s center, so its angular momentum about the Earth’s center is conserved.
296. In which of the following cases is angular momentum NOT conserved?
ⓐ. A planet orbiting the sun
ⓑ. A skater pulling in their arms
ⓒ. A spinning top on a rough surface experiencing friction
ⓓ. A freely rotating wheel in space
Correct Answer: A spinning top on a rough surface experiencing friction
Explanation: External torque due to friction acts on the spinning top, so angular momentum is not conserved. In the other cases, external torque is absent, ensuring conservation.
297. A body of moment of inertia \(I\) is rotating with angular velocity \(\omega\). If its moment of inertia changes to \(I/2\) without external torque, its new angular velocity will be:
ⓐ. \(\omega/2\)
ⓑ. \(\omega\)
ⓒ. \(2\omega\)
ⓓ. \(4\omega\)
Correct Answer: \(2\omega\)
Explanation: Angular momentum conservation gives \(I \omega = I’ \omega’\). Substituting \(I’ = I/2\): \(\omega’ = (I \omega) / (I/2) = 2\omega\). Thus angular velocity doubles.
298. A neutron star forms when a massive star collapses. Its angular velocity becomes extremely high because:
ⓐ. Its mass decreases
ⓑ. Its radius decreases, reducing moment of inertia
ⓒ. It gains extra torque from gravity
ⓓ. Its temperature increases
Correct Answer: Its radius decreases, reducing moment of inertia
Explanation: As the star’s radius shrinks, its moment of inertia reduces drastically. With angular momentum conserved, \(\omega\) increases significantly, leading to very high rotation rates of neutron stars.
299. Which equation best expresses conservation of angular momentum?
ⓐ. \(I_1 \omega_1 = I_2 \omega_2\)
ⓑ. \(I \alpha = \tau\)
ⓒ. \(F = ma\)
ⓓ. \(L = mvr\)
Correct Answer: \(I_1 \omega_1 = I_2 \omega_2\)
Explanation: If no external torque acts, angular momentum remains constant. Thus, the initial angular momentum \(I_1 \omega_1\) equals the final angular momentum \(I_2 \omega_2\).
300. Which of the following is a practical example of conservation of angular momentum?
ⓐ. A book lying on a table
ⓑ. A bullet fired from a gun
ⓒ. A gymnast performing a somersault and curling into a ball to spin faster
ⓓ. A car accelerating in a straight line
Correct Answer: A gymnast performing a somersault and curling into a ball to spin faster
Explanation: By curling, the gymnast reduces moment of inertia. Since no external torque acts, angular momentum remains conserved, so angular velocity increases. This is a classic real-life application of the conservation of angular momentum principle.
The topic System of Particles and Rotational Motion is a high-weightage chapter in NCERT/CBSE Class 11 Physics, making it crucial for success in both board exams and competitive exams like JEE, NEET, and other entrance tests. It includes advanced ideas like angular velocity, angular acceleration, rotational kinetic energy, and practical applications of rotational motion. Across all 6 parts, there are 570 MCQs with answers, designed to strengthen both theory and application skills. In this section, you will practice the third set of 100 MCQs with explanations, useful for mastering conceptual and numerical questions.
- 👉 Total MCQs in this chapter: 570.
- 👉 This page contains: Third set of 100 solved MCQs.
- 👉 Highly useful for board exams, JEE, NEET, and state competitive exams.
- 👉 To explore more chapters, subjects, or classes, check the top navigation bar.
- 👉 To proceed further, click the Part 4 button above.