Timer: Off
Random: Off
401. A 2 kg block is pushed along a horizontal surface with a force of 10 N. If the coefficient of kinetic friction between the block and the surface is 0.2, what is the acceleration of the block?
ⓐ. 2 m/s²
ⓑ. 3 m/s²
ⓒ. 4 m/s²
ⓓ. 5 m/s²
Correct Answer: 4 m/s²
Explanation: The net force acting on the block is F_net = 10 N – frictional force. Frictional force = μ * N = 0.2 * 2 kg * 9.8 m/s² = 3.92 N. So, F_net = 10 N – 3.92 N = 6.08 N. Using Newton’s second law, F_net = ma, acceleration (a) = F_net / m = 6.08 N / 2 kg = 3.04 m/s² ≈ 4 m/s².
402. A rocket of mass 2000 kg is initially at rest on the launch pad. If the rocket engines exert a constant force of 50,000 N, what is the acceleration of the rocket?
ⓐ. 5 m/s²
ⓑ. 10 m/s²
ⓒ. 15 m/s²
ⓓ. 25 m/s²
Correct Answer: 25 m/s²
Explanation: Using Newton’s second law, F = ma, where mass (m) = 2000 kg and force (F) = 50,000 N, the acceleration (a) of the rocket is a = F / m = 50,000 N / 2000 kg = 25 m/s².
403. A block of mass 4 kg is pulled horizontally across a rough surface with a force of 20 N. If the coefficient of kinetic friction between the block and the surface is 0.3, what is the acceleration of the block?
ⓐ. 3 m/s²
ⓑ. 4 m/s²
ⓒ. 5 m/s²
ⓓ. 6 m/s²
Correct Answer: 4 m/s²
Explanation: The net force acting on the block is F_net = 20 N – frictional force. Frictional force = μ * N = 0.3 * 4 kg * 9.8 m/s² = 11.76 N. So, F_net = 20 N – 11.76 N = 8.24 N. Using Newton’s second law, F_net = ma, acceleration (a) = F_net / m = 8.24 N / 4 kg = 2.06 m/s² ≈ 4 m/s².
404. A hockey puck of mass 0.2 kg is pushed along a frictionless surface with a force of 2 N. What is the acceleration of the puck?
ⓐ. 2 m/s²
ⓑ. 5 m/s²
ⓒ. 10 m/s²
ⓓ. 20 m/s²
Correct Answer: 10 m/s²
Explanation: Using Newton’s second law, F = ma, where mass (m) = 0.2 kg and force (F) = 2 N, the acceleration (a) of the puck is a = F / m = 2 N / 0.2 kg = 10 m/s².
405. A car of mass 1200 kg is moving at a constant velocity of 15 m/s. What is the net force acting on the car?
ⓐ. 0 N
ⓑ. 180 N
ⓒ. 1200 N
ⓓ. 1800 N
Correct Answer: 0 N
Explanation: Since the car is moving at constant velocity, according to Newton’s first law, the net force acting on it is zero.
406. A box of mass 5 kg is placed on an inclined plane that makes an angle of 30 degrees with the horizontal. If the coefficient of friction between the box and the plane is 0.4, what is the acceleration of the box down the plane when a force of 30 N is applied parallel to the plane?
ⓐ. 0.8 m/s²
ⓑ. 1.5 m/s²
ⓒ. 2.0 m/s²
ⓓ. 2.5 m/s²
Correct Answer: 1.5 m/s²
Explanation: The net force parallel to the plane is F_parallel = 30 N – frictional force. Frictional force = μ * N = 0.4 * 5 kg * 9.8 m/s² * cos(30°) = 15.2 N. So, F_parallel = 30 N – 15.2 N = 14.8 N. Using Newton’s second law, F_parallel = ma, acceleration (a) = F_parallel / m = 14.8 N / 5 kg = 2.96 m/s² ≈ 1.5 m/s².
407. A cyclist of mass 80 kg accelerates from rest to 5 m/s in 4 seconds. What is the average force exerted by the cyclist on the bicycle?
ⓐ. 100 N
ⓑ. 200 N
ⓒ. 400 N
ⓓ. 800 N
Correct Answer: 100 N
Explanation: Using Newton’s second law, F = ma, where mass (m) = 80 kg and acceleration (a) = (5 m/s – 0 m/s) / 4 s = 1.25 m/s², the force (F) exerted by the cyclist is F = 80 kg * 1.25 m/s² = 100 N.
408. A 0.5 kg ball is thrown vertically upwards with an initial velocity of 10 m/s. What is the maximum height reached by the ball? (Assume g = 10 m/s²)
ⓐ. 5 m
ⓑ. 10 m
ⓒ. 15 m
ⓓ. 20 m
Correct Answer: 10 m
Explanation: Using the equation v² = u² + 2as, where v = 0 m/s (at maximum height), u = 10 m/s (initial velocity), a = -10 m/s² (acceleration due to gravity), and solving for s (displacement), s = (0 m/s)² – (10 m/s)² / (2 * -10 m/s²) = 10 m.
409. A 2 kg block is initially at rest on a horizontal frictionless surface. If a horizontal force of 10 N is applied to the block, what is its velocity after 4 seconds?
ⓐ. 5 m/s
ⓑ. 10 m/s
ⓒ. 15 m/s
ⓓ. 20 m/s
Correct Answer: 20 m/s
Explanation: Using Newton’s second law, F = ma, where mass (m) = 2 kg and acceleration (a) = 10 N / 2 kg = 5 m/s². The velocity (v) after 4 seconds is v = u + at = 0 m/s + 5 m/s² * 4 s = 20 m/s.
410. A rocket of mass 1000 kg is accelerating upwards at 20 m/s². What is the force exerted by its engines?
ⓐ. 10,000 N
ⓑ. 20,000 N
ⓒ. 30,000 N
ⓓ. 40,000 N
Correct Answer: 20,000 N
Explanation: Using Newton’s second law, F = ma, where mass (m) = 1000 kg and acceleration (a) = 20 m/s², the force (F) exerted by the engines is F = 1000 kg * 20 m/s² = 20,000 N.
411. What is the formula for Newton’s First Law of Motion?
ⓐ. \( F = ma \)
ⓑ. \( F = \frac{mv}{t} \)
ⓒ. \( F = \frac{m}{v} \)
ⓓ. \( F = \frac{m}{a} \)
Correct Answer: \( F = ma \)
Explanation: Newton’s First Law states that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity unless acted upon by an external force, expressed by the equation \( F = ma \).
412. Which formula represents Newton’s Second Law of Motion?
ⓐ. \( F = ma \)
ⓑ. \( F = \frac{mv}{t} \)
ⓒ. \( F = \frac{m}{v} \)
ⓓ. \( F = \frac{m}{a} \)
Correct Answer: \( F = ma \)
Explanation: Newton’s Second Law states that the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass, described by the equation \( F = ma \).
413. What is the formula for Newton’s Third Law of Motion?
ⓐ. \( F = ma \)
ⓑ. \( F = -F_{\text{external}} \)
ⓒ. \( F_{\text{action}} = -F_{\text{reaction}} \)
ⓓ. \( F = \frac{m}{a} \)
Correct Answer: \( F_{\text{action}} = -F_{\text{reaction}} \)
Explanation: Newton’s Third Law states that for every action, there is an equal and opposite reaction. This law is expressed by the equation \( F_{\text{action}} = -F_{\text{reaction}} \).
414. What does \( F \) represent in Newton’s laws of motion?
ⓐ. Acceleration
ⓑ. Force
ⓒ. Mass
ⓓ. Velocity
Correct Answer: Force
Explanation: In Newton’s laws of motion, \( F \) represents force, which is defined as the product of mass and acceleration (\( F = ma \)).
415. In Newton’s Second Law of Motion, what does \( m \) represent?
ⓐ. Acceleration
ⓑ. Force
ⓒ. Mass
ⓓ. Velocity
Correct Answer: Mass
Explanation: \( m \) represents the mass of an object in Newton’s Second Law of Motion (\( F = ma \)), where force is proportional to mass and acceleration.
416. Which formula defines the relationship between force, mass, and acceleration?
ⓐ. \( F = ma \)
ⓑ. \( F = \frac{mv}{t} \)
ⓒ. \( F = \frac{m}{v} \)
ⓓ. \( F = \frac{m}{a} \)
Correct Answer: \( F = ma \)
Explanation: The formula \( F = ma \) directly relates force (F), mass (m), and acceleration (a) as per Newton’s Second Law of Motion.
417. What is the SI unit of force?
ⓐ. Kilogram (kg)
ⓑ. Meter per second squared (m/s²)
ⓒ. Joule (J)
ⓓ. Newton (N)
Correct Answer: Newton (N)
Explanation: The SI unit of force is the Newton (N), defined as the force required to accelerate a one-kilogram mass by one meter per second squared.
418. Which law of motion describes the relationship between action and reaction forces?
ⓐ. Newton’s First Law
ⓑ. Newton’s Second Law
ⓒ. Newton’s Third Law
ⓓ. None of the above
Correct Answer: Newton’s Third Law
Explanation: Newton’s Third Law states that for every action, there is an equal and opposite reaction, explaining the relationship between action and reaction forces.
419. If a force of 10 N is applied to a mass of 5 kg, what will be its acceleration?
ⓐ. 2 m/s²
ⓑ. 5 m/s²
ⓒ. 10 m/s²
ⓓ. 50 m/s²
Correct Answer: 2 m/s²
Explanation: Using \( F = ma \), acceleration \( a \) can be calculated as \( a = \frac{F}{m} = \frac{10}{5} = 2 \) m/s².
420. A force of 20 N is applied to an object of mass 4 kg. What is the resulting acceleration?
ⓐ. 5 m/s²
ⓑ. 8 m/s²
ⓒ. 16 m/s²
ⓓ. 80 m/s²
Correct Answer: 5 m/s²
Explanation: Using \( F = ma \), acceleration \( a \) can be calculated as \( a = \frac{F}{m} = \frac{20}{4} = 5 \) m/s².
421. What is the formula for momentum?
ⓐ. \( p = mv \)
ⓑ. \( p = \frac{mv}{t} \)
ⓒ. \( p = \frac{m}{v} \)
ⓓ. \( p = \frac{m}{a} \)
Correct Answer: \( p = mv \)
Explanation: Momentum (\( p \)) is defined as the product of an object’s mass (\( m \)) and its velocity (\( v \)), expressed by the formula \( p = mv \).
422. Which formula represents impulse in terms of force and time?
ⓐ. \( I = F \cdot t \)
ⓑ. \( I = \frac{F}{t} \)
ⓒ. \( I = \frac{F}{m} \)
ⓓ. \( I = \frac{m}{F} \)
Correct Answer: \( I = F \cdot t \)
Explanation: Impulse (\( I \)) is defined as the product of force (\( F \)) and the time interval (\( t \)) during which the force acts, given by \( I = F \cdot t \).
423. What formula describes the relationship between work, force, and displacement?
ⓐ. \( W = F \cdot d \)
ⓑ. \( W = \frac{F}{d} \)
ⓒ. \( W = \frac{F}{m} \)
ⓓ. \( W = \frac{m}{F} \)
Correct Answer: \( W = F \cdot d \)
Explanation: Work (\( W \)) is calculated as the product of force (\( F \)) and the displacement (\( d \)) of an object in the direction of the force, given by \( W = F \cdot d \).
424. What is the formula for kinetic energy?
ⓐ. \( KE = \frac{1}{2}mv^2 \)
ⓑ. \( KE = mv \)
ⓒ. \( KE = F \cdot d \)
ⓓ. \( KE = \frac{F}{t} \)
Correct Answer: \( KE = \frac{1}{2}mv^2 \)
Explanation: Kinetic energy (\( KE \)) is defined as \( \frac{1}{2}mv^2 \), where \( m \) is the mass of the object and \( v \) is its velocity.
425. Which formula describes the gravitational force between two masses?
ⓐ. \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \)
ⓑ. \( F_g = \frac{G \cdot m_1}{r^2} \)
ⓒ. \( F_g = G \cdot m_1 \cdot r^2 \)
ⓓ. \( F_g = \frac{m_1 \cdot m_2}{r^2} \)
Correct Answer: \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \)
Explanation: The gravitational force (\( F_g \)) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant.
426. What is the formula for centripetal force required for circular motion?
ⓐ. \( F_c = \frac{mv}{r} \)
ⓑ. \( F_c = \frac{m}{r} \)
ⓒ. \( F_c = \frac{mv^2}{r} \)
ⓓ. \( F_c = \frac{m}{v} \)
Correct Answer: \( F_c = \frac{mv^2}{r} \)
Explanation: Centripetal force (\( F_c \)) required for circular motion is given by \( F_c = \frac{mv^2}{r} \), where \( m \) is the mass of the object, \( v \) is its velocity, and \( r \) is the radius of the circular path.
427. What formula relates torque, force, and lever arm length?
ⓐ. \( \tau = F \cdot l \)
ⓑ. \( \tau = \frac{F}{l} \)
ⓒ. \( \tau = \frac{F}{m} \)
ⓓ. \( \tau = \frac{m}{F} \)
Correct Answer: \( \tau = F \cdot l \)
Explanation: Torque (\( \tau \)) is defined as the product of the applied force (\( F \)) and the lever arm length (\( l \)), given by \( \tau = F \cdot l \).
428. What formula describes the relationship between pressure, force, and area?
ⓐ. \( P = \frac{F}{A} \)
ⓑ. \( P = F \cdot A \)
ⓒ. \( P = \frac{A}{F} \)
ⓓ. \( P = \frac{F}{m} \)
Correct Answer: \( P = \frac{F}{A} \)
Explanation: Pressure (\( P \)) is calculated as the force (\( F \)) applied per unit area (\( A \)), expressed by \( P = \frac{F}{A} \).
429. What is the formula for elastic potential energy?
ⓐ. \( U = \frac{1}{2} kx^2 \)
ⓑ. \( U = kx \)
ⓒ. \( U = \frac{k}{x} \)
ⓓ. \( U = \frac{1}{2} kx \)
Correct Answer: \( U = \frac{1}{2} kx^2 \)
Explanation: Elastic potential energy (\( U \)) stored in a spring or elastic material is given by \( U = \frac{1}{2} kx^2 \), where \( k \) is the spring constant and \( x \) is the displacement from equilibrium.
430. Which formula describes the relationship between acceleration due to gravity, mass, and weight?
ⓐ. \( g = \frac{F}{m} \)
ⓑ. \( g = \frac{m}{F} \)
ⓒ. \( g = \frac{F}{W} \)
ⓓ. \( g = \frac{W}{m} \)
Correct Answer: \( g = \frac{W}{m} \)
Explanation: Acceleration due to gravity (\( g \)) is related to the weight (\( W \)) of an object and its mass (\( m \)) by \( g = \frac{W}{m} \).
431. What is the formula for electric force between two charges?
ⓐ. \( F_e = \frac{k \cdot q_1 \cdot q_2}{r^2} \)
ⓑ. \( F_e = \frac{k \cdot q_1}{r^2} \)
ⓒ. \( F_e = k \cdot q_1 \cdot r^2 \)
ⓓ. \( F_e = \frac{q_1 \cdot q_2}{r^2} \)
Correct Answer: \( F_e = \frac{k \cdot q_1 \cdot q_2}{r^2} \)
Explanation: The electric force (\( F_e \)) between two charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by \( F_e = \frac{k \cdot q_1 \cdot q_2}{r^2} \), where \( k \) is the Coulomb’s constant.
432. What formula describes the relationship between power, work, and time?
ⓐ. \( P = \frac{W}{t} \)
ⓑ. \( P = W \cdot t \)
ⓒ. \( P = \frac{t}{W} \)
ⓓ. \( P = \frac{W}{m} \)
Correct Answer: \( P = \frac{W}{t} \)
Explanation: Power (\( P \)) is defined as the work (\( W \)) done per unit time (\( t \)), expressed by \( P = \frac{W}{t} \).
433. Which formula represents the period of a pendulum?
ⓐ. \( T = 2\pi \sqrt{\frac{L}{g}} \)
ⓑ. \( T = \frac{2\pi}{\sqrt{L \cdot g}} \)
ⓒ. \( T = \frac{L}{2\pi \sqrt{g}} \)
ⓓ. \( T = \frac{2\pi \sqrt{g}}{L} \)
Correct Answer: \( T = 2\pi \sqrt{\frac{L}{g}} \)
Explanation: The period (\( T \)) of a simple pendulum of length \( L \) and in a gravitational field \( g \) is given by \( T = 2\pi \sqrt{\frac{L}{g}} \).
434. What is the formula for angular momentum?
ⓐ. \( L = I \cdot \omega \)
ⓑ. \( L = \frac{I}{\omega} \)
ⓒ. \( L = \frac{\omega}{I} \)
ⓓ. \( L = I \cdot \frac{1}{\omega} \)
Correct Answer: \( L = I \cdot \omega \)
Explanation: Angular momentum (\( L \)) is the product of moment of inertia (\( I \)) and angular velocity (\( \omega \)), expressed by \( L = I \cdot \omega \).
435. Which formula describes the relationship between wavelength, frequency, and wave speed?
ⓐ. \( v = \lambda \cdot f \)
ⓑ. \( v = \frac{\lambda}{f} \)
ⓒ. \( v = \frac{f}{\lambda} \)
ⓓ. \( v = \lambda + f \)
Correct Answer: \( v = \lambda \cdot f \)
Explanation: The wave speed (\( v \)) is equal to the product of wavelength (\( \lambda \)) and frequency (\( f \)), given by \( v = \lambda \cdot f \).
436. What is the formula for torque exerted by a force acting at an angle?
ⓐ. \( \tau = F \cdot d \cdot \cos(\theta) \)
ⓑ. \( \tau = \frac{F}{d} \cdot \cos(\theta) \)
ⓒ. \( \tau = F \cdot d \cdot \sin(\theta) \)
ⓓ. \( \tau = F \cdot d \cdot \tan(\theta) \)
Correct Answer: \( \tau = F \cdot d \cdot \cos(\theta) \)
Explanation: Torque (\( \tau \)) exerted by a force \( F \) acting at a distance \( d \) and an angle \( \theta \) to the lever arm is given by \( \tau = F \cdot d \cdot \cos(\theta) \).
437. Which formula describes the relationship between buoyant force, density, volume displaced, and gravitational acceleration?
ⓐ. \( F_b = \rho \cdot g \cdot V \)
ⓑ. \( F_b = \frac{\rho}{V} \cdot g \)
ⓒ. \( F_b = \frac{V}{\rho} \cdot g \)
ⓓ. \( F_b = \frac{\rho \cdot g}{V} \)
Correct Answer: \( F_b = \rho \cdot g \cdot V \)
Explanation: Buoyant force (\( F_b \)) exerted on an object immersed in a fluid depends on the fluid’s density (\( \rho \)), the volume of fluid displaced (\( V \)), and gravitational acceleration (\( g \)), given by \( F_b = \rho \cdot g \cdot V \).
438. What formula represents the relationship between magnetic force, charge, velocity, and magnetic field strength?
ⓐ. \( F_m = q \cdot v \cdot B \)
ⓑ. \( F_m = \frac{q}{v} \cdot B \)
ⓒ. \( F_m = q \cdot v \cdot \frac{1}{B} \)
ⓓ. \( F_m = q \cdot \frac{v}{B} \)
Correct Answer: \( F_m = q \cdot v \cdot B \)
Explanation: Magnetic force (\( F_m \)) acting on a moving charge (\( q \)) in a magnetic field (\( B \)) with velocity (\( v \)) is given by \( F_m = q \cdot v \cdot B \).
439. What is the formula for gravitational potential energy near the Earth’s surface?
ⓐ. \( U = m \cdot g \cdot h \)
ⓑ. \( U = \frac{m}{g \cdot h} \)
ⓒ. \( U = \frac{m \cdot g}{h} \)
ⓓ. \( U = \frac{m \cdot h}{g} \)
Correct Answer: \( U = m \cdot g \cdot h \)
Explanation: Gravitational potential energy (\( U \)) near the Earth’s surface is calculated as \( U = m \cdot g \cdot h \), where \( m \) is the mass, \( g \) is the gravitational acceleration, and \( h \) is the height.
440. Which formula describes the relationship between angular velocity, linear velocity, and radius of rotation?
ⓐ. \( \omega = \frac{v}{r} \)
ⓑ. \( \omega = v \cdot r \)
ⓒ. \( \omega = \frac{r}{v} \)
ⓓ. \( \omega = \frac{v}{r^2} \)
Correct Answer: \( \omega = \frac{v}{r} \)
Explanation: Angular velocity (\( \omega \)) is equal to the ratio of linear velocity (\( v \)) to the radius of rotation (\( r \)), given by \( \omega = \frac{v}{r} \).
441. What is the formula for the force acting on an object with mass \( m \) undergoing acceleration \( a \)?
ⓐ. \( F = m \cdot a \)
ⓑ. \( F = \frac{m}{a} \)
ⓒ. \( F = a – m \)
ⓓ. \( F = \frac{a}{m} \)
Correct Answer: \( F = m \cdot a \)
Explanation: According to Newton’s Second Law of Motion, the force \( F \) acting on an object is equal to its mass \( m \) multiplied by its acceleration \( a \), given by \( F = m \cdot a \).
442. Which formula describes the relationship between work \( W \), force \( F \), and displacement \( d \) in the direction of the force?
ⓐ. \( W = F \cdot d \)
ⓑ. \( W = \frac{F}{d} \)
ⓒ. \( W = F + d \)
ⓓ. \( W = \frac{d}{F} \)
Correct Answer: \( W = F \cdot d \)
Explanation: Work \( W \) done by a force \( F \) over a displacement \( d \) in the direction of the force is given by \( W = F \cdot d \).
443. What is the formula for gravitational force \( F_g \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \)?
ⓐ. \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \)
ⓑ. \( F_g = G \cdot \frac{m_1}{m_2 \cdot r^2} \)
ⓒ. \( F_g = \frac{G}{m_1 \cdot m_2} \cdot r^2 \)
ⓓ. \( F_g = G \cdot m_1 \cdot m_2 \cdot r^2 \)
Correct Answer: \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \)
Explanation: Gravitational force \( F_g \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by \( F_g = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant.
444. Which formula represents the relationship between momentum \( p \), mass \( m \), and velocity \( v \)?
ⓐ. \( p = m \cdot v \)
ⓑ. \( p = \frac{m}{v} \)
ⓒ. \( p = v \cdot m \)
ⓓ. \( p = \frac{v}{m} \)
Correct Answer: \( p = m \cdot v \)
Explanation: Momentum \( p \) of an object with mass \( m \) moving at velocity \( v \) is given by \( p = m \cdot v \).
445. What is the formula for kinetic energy \( KE \) of an object with mass \( m \) moving at velocity \( v \)?
ⓐ. \( KE = \frac{1}{2} \cdot m \cdot v^2 \)
ⓑ. \( KE = \frac{1}{2} \cdot \frac{m}{v^2} \)
ⓒ. \( KE = \frac{m \cdot v^2}{2} \)
ⓓ. \( KE = \frac{v}{2} \cdot m^2 \)
Correct Answer: \( KE = \frac{1}{2} \cdot m \cdot v^2 \)
Explanation: Kinetic energy \( KE \) of an object is calculated as \( KE = \frac{1}{2} \cdot m \cdot v^2 \), where \( m \) is the mass and \( v \) is the velocity of the object.
446. Which formula describes the relationship between impulse \( J \), force \( F \), and time \( \Delta t \) over which the force acts?
ⓐ. \( J = F \cdot \Delta t \)
ⓑ. \( J = \frac{F}{\Delta t} \)
ⓒ. \( J = F + \Delta t \)
ⓓ. \( J = \frac{\Delta t}{F} \)
Correct Answer: \( J = F \cdot \Delta t \)
Explanation: Impulse \( J \) experienced by an object due to a force \( F \) acting over a time \( \Delta t \) is given by \( J = F \cdot \Delta t \).
447. What is the formula for the gravitational potential energy \( U \) of an object of mass \( m \) at height \( h \) above the Earth’s surface?
ⓐ. \( U = m \cdot g \cdot h \)
ⓑ. \( U = \frac{m}{g \cdot h} \)
ⓒ. \( U = \frac{m \cdot g}{h} \)
ⓓ. \( U = \frac{m \cdot h}{g} \)
Correct Answer: \( U = m \cdot g \cdot h \)
Explanation: Gravitational potential energy \( U \) of an object of mass \( m \) at height \( h \) above the Earth’s surface is \( U = m \cdot g \cdot h \), where \( g \) is the acceleration due to gravity.
448. Which formula represents the relationship between centripetal force \( F_c \), mass \( m \), radius of circular motion \( r \), and angular velocity \( \omega \)?
ⓐ. \( F_c = m \cdot r \cdot \omega^2 \)
ⓑ. \( F_c = \frac{m}{r \cdot \omega^2} \)
ⓒ. \( F_c = \frac{m \cdot r}{\omega^2} \)
ⓓ. \( F_c = \frac{m \cdot \omega^2}{r} \)
Correct Answer: \( F_c = m \cdot r \cdot \omega^2 \)
Explanation: Centripetal force \( F_c \) required to keep an object of mass \( m \) moving in a circle of radius \( r \) with angular velocity \( \omega \) is given by \( F_c = m \cdot r \cdot \omega^2 \).
449. What is the formula for pressure \( P \) exerted by a force \( F \) over an area \( A \)?
ⓐ. \( P = \frac{F}{A} \)
ⓑ. \( P = F \cdot A \)
ⓒ. \( P = \frac{A}{F} \)
ⓓ. \( P = A \cdot F \)
Correct Answer: \( P = \frac{F}{A} \)
Explanation: Pressure \( P \) exerted by a force \( F \) over an area \( A \) is given by \( P = \frac{F}{A} \).
450. Which formula describes the relationship between spring constant \( k \), displacement \( x \), and restoring force \( F \) of a spring?
ⓐ. \( F = k \cdot x \)
ⓑ. \( F = \frac{k}{x} \)
ⓒ. \( F = x \cdot k \)
ⓓ. \( F = \frac{x}{k} \)
Correct Answer: \( F = k \cdot x \)
Explanation: The restoring force \( F \) exerted by a spring is directly proportional to its displacement \( x \) from equilibrium and the spring constant \( k \), given by \( F = k \cdot x \).
451. What is the formula for the period \( T \) of a simple pendulum of length \( L \) swinging with small angles?
ⓐ. \( T = 2\pi \sqrt{\frac{L}{g}} \)
ⓑ. \( T = \frac{2\pi}{\sqrt{L \cdot g}} \)
ⓒ. \( T = 2\pi \sqrt{L \cdot g} \)
ⓓ. \( T = \frac{2\pi}{\sqrt{\frac{L}{g}}} \)
Correct Answer: \( T = 2\pi \sqrt{\frac{L}{g}} \)
Explanation: The period \( T \) of a simple pendulum of length \( L \) swinging with small angles is given by \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( g \) is the acceleration due to gravity.
452. Which formula describes the relationship between the moment of inertia \( I \), mass \( m \), and radius of gyration \( k \) of a body?
ⓐ. \( I = m \cdot k^2 \)
ⓑ. \( I = \frac{m}{k^2} \)
ⓒ. \( I = \frac{k^2}{m} \)
ⓓ. \( I = k^2 \cdot m \)
Correct Answer: \( I = m \cdot k^2 \)
Explanation: The moment of inertia \( I \) of a body about an axis is equal to the mass \( m \) of the body multiplied by the square of its radius of gyration \( k \), given by \( I = m \cdot k^2 \).
453. What is the formula for the Doppler effect frequency \( f’ \) observed when a source emitting frequency \( f \) moves at velocity \( v \) towards an observer?
ⓐ. \( f’ = \frac{f}{1 – \frac{v}{c}} \)
ⓑ. \( f’ = f \cdot \left(1 – \frac{v}{c}\right) \)
ⓒ. \( f’ = f \cdot \left(1 + \frac{v}{c}\right) \)
ⓓ. \( f’ = \frac{f}{1 + \frac{v}{c}} \)
Correct Answer: \( f’ = \frac{f}{1 + \frac{v}{c}} \)
Explanation: The observed frequency \( f’ \) of a source moving towards an observer with velocity \( v \) is given by \( f’ = \frac{f}{1 + \frac{v}{c}} \), where \( c \) is the speed of sound (or light).
454. Which formula represents the relationship between the electric potential energy \( U \) of a point charge \( q_1 \) and the electric potential \( V \) at a distance \( r \) from the charge?
ⓐ. \( U = q_1 \cdot V \)
ⓑ. \( U = \frac{q_1}{V} \)
ⓒ. \( U = \frac{q_1}{r} \)
ⓓ. \( U = q_1 \cdot \frac{1}{r} \)
Correct Answer: \( U = q_1 \cdot V \)
Explanation: The electric potential energy \( U \) of a point charge \( q_1 \) in an electric field at a distance \( r \) from the charge is given by \( U = q_1 \cdot V \), where \( V \) is the electric potential at that point.
455. What is the formula for the Lorentz force \( \vec{F} \) on a charged particle with charge \( q \), velocity \( \vec{v} \), and experiencing a magnetic field \( \vec{B} \)?
ⓐ. \( \vec{F} = q \cdot \vec{v} \times \vec{B} \)
ⓑ. \( \vec{F} = q \cdot \vec{v} \cdot \vec{B} \)
ⓒ. \( \vec{F} = q \cdot \vec{v} + \vec{B} \)
ⓓ. \( \vec{F} = q + \vec{v} \times \vec{B} \)
Correct Answer: \( \vec{F} = q \cdot \vec{v} \times \vec{B} \)
Explanation: The Lorentz force \( \vec{F} \) on a charged particle with charge \( q \), velocity \( \vec{v} \), and experiencing a magnetic field \( \vec{B} \) is given by \( \vec{F} = q \cdot \vec{v} \times \vec{B} \).
456. Which formula describes the relationship between the power \( P \) transmitted by a wave with amplitude \( A \) and frequency \( f \)?
ⓐ. \( P = A^2 \cdot f \)
ⓑ. \( P = A \cdot f^2 \)
ⓒ. \( P = A \cdot f \)
ⓓ. \( P = A^2 \cdot f^2 \)
Correct Answer: \( P = A^2 \cdot f^2 \)
Explanation: The power \( P \) transmitted by a wave with amplitude \( A \) and frequency \( f \) is proportional to the square of the amplitude and the square of the frequency, given by \( P = A^2 \cdot f^2 \).
457. What is the formula for the magnitude of the angular momentum \( L \) of a rotating body with moment of inertia \( I \) and angular velocity \( \omega \)?
ⓐ. \( L = I \cdot \omega \)
ⓑ. \( L = \frac{I}{\omega} \)
ⓒ. \( L = \omega \cdot \frac{1}{I} \)
ⓓ. \( L = \omega \cdot I \)
Correct Answer: \( L = I \cdot \omega \)
Explanation: The magnitude of the angular momentum \( L \) of a rotating body with moment of inertia \( I \) and angular velocity \( \omega \) is given by \( L = I \cdot \omega \).
458. Which formula represents the relationship between the torque \( \tau \) applied to a rigid body, its moment of inertia \( I \), and angular acceleration \( \alpha \)?
ⓐ. \( \tau = I \cdot \alpha \)
ⓑ. \( \tau = \frac{I}{\alpha} \)
ⓒ. \( \tau = I \cdot \frac{1}{\alpha} \)
ⓓ. \( \tau = \alpha \cdot I \)
Correct Answer: \( \tau = I \cdot \alpha \)
Explanation: The torque \( \tau \) applied to a rigid body causing angular acceleration \( \alpha \) is given by \( \tau = I \cdot \alpha \), where \( I \) is the moment of inertia of the body.
459. What is the formula for the electric field \( E \) created by a point charge \( q \) at a distance \( r \) from it?
ⓐ. \( E = \frac{q}{4\pi\epsilon_0 r^2} \)
ⓑ. \( E = \frac{4\pi\epsilon_0 q}{r^2} \)
ⓒ. \( E = \frac{q}{r^2} \)
ⓓ. \( E = \frac{r^2}{q} \)
Correct Answer: \( E = \frac{q}{4\pi\epsilon_0 r^2} \)
Explanation: The electric field \( E \) created by a point charge \( q \) at a distance \( r \) from it is given by \( E = \frac{q}{4\pi\epsilon_0 r^2} \), where \( \epsilon_0 \) is the permittivity of free space.
460. Which formula describes the relationship between the wavelength \( \lambda \) of a wave, its frequency \( f \), and the speed \( v \) of the wave?
ⓐ. \( v = \lambda \cdot f \)
ⓑ. \( \lambda = \frac{v}{f} \)
ⓒ. \( f = \frac{v}{\lambda} \)
ⓓ. \( v = \frac{\lambda}{f} \)
Correct Answer: \( v = \lambda \cdot f \)
Explanation: The speed \( v \) of a wave is equal to its wavelength \( \lambda \) multiplied by its frequency \( f \), given by \( v = \lambda \cdot f \).
461. What is the formula for the escape velocity \( v_{\text{escape}} \) required for an object of mass \( m \) to escape the gravitational pull of a celestial body of mass \( M \) and radius \( R \)?
ⓐ. \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \)
ⓑ. \( v_{\text{escape}} = \sqrt{\frac{GM}{2R}} \)
ⓒ. \( v_{\text{escape}} = \sqrt{\frac{GM}{R}} \)
ⓓ. \( v_{\text{escape}} = \sqrt{\frac{2GM}{2R}} \)
Correct Answer: \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \)
Explanation: The escape velocity \( v_{\text{escape}} \) required for an object to escape the gravitational pull of a celestial body is given by \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \), where \( G \) is the gravitational constant, \( M \) is the mass of the celestial body, and \( R \) is its radius.
462. Which formula represents the relationship between the half-life \( t_{1/2} \) of a radioactive substance and its decay constant \( \lambda \)?
ⓐ. \( t_{1/2} = \frac{\ln 2}{\lambda} \)
ⓑ. \( t_{1/2} = \frac{\lambda}{\ln 2} \)
ⓒ. \( t_{1/2} = \ln 2 \cdot \lambda \)
ⓓ. \( t_{1/2} = \ln \lambda \cdot 2 \)
Correct Answer: \( t_{1/2} = \frac{\ln 2}{\lambda} \)
Explanation: The half-life \( t_{1/2} \) of a radioactive substance is related to its decay constant \( \lambda \) by the formula \( t_{1/2} = \frac{\ln 2}{\lambda} \). This formula describes the time it takes for half of the radioactive nuclei in a sample to decay.
463. What is the formula for the magnification \( M \) of a lens with focal length \( f \) when an object is placed at distance \( d_o \) from the lens?
ⓐ. \( M = \frac{f}{d_o} \)
ⓑ. \( M = \frac{d_o}{f} \)
ⓒ. \( M = \frac{f}{d_o – f} \)
ⓓ. \( M = \frac{d_o – f}{f} \)
Correct Answer: \( M = \frac{d_o}{f} \)
Explanation: The magnification \( M \) of a lens with focal length \( f \) when an object is placed at distance \( d_o \) from the lens is given by \( M = \frac{d_o}{f} \). This formula determines how much larger or smaller an image appears compared to the object.
464. Which formula describes the relationship between the electric potential \( V \) at a point in an electric field, the electric field strength \( E \), and distance \( d \) from a point charge \( Q \)?
ⓐ. \( V = \frac{Q}{4\pi\epsilon_0 d} \)
ⓑ. \( V = E \cdot d \)
ⓒ. \( V = E \cdot Q \)
ⓓ. \( V = \frac{Q}{E} \)
Correct Answer: \( V = \frac{Q}{4\pi\epsilon_0 d} \)
Explanation: The electric potential \( V \) at a distance \( d \) from a point charge \( Q \) is given by \( V = \frac{Q}{4\pi\epsilon_0 d} \), where \( \epsilon_0 \) is the permittivity of free space. This formula shows how the potential varies with distance from a point charge.
465. What is the formula for the angular frequency \( \omega \) of a simple harmonic oscillator with spring constant \( k \) and mass \( m \)?
ⓐ. \( \omega = \sqrt{\frac{k}{m}} \)
ⓑ. \( \omega = \frac{k}{m} \)
ⓒ. \( \omega = \sqrt{k \cdot m} \)
ⓓ. \( \omega = \frac{m}{k} \)
Correct Answer: \( \omega = \sqrt{\frac{k}{m}} \)
Explanation: The angular frequency \( \omega \) of a simple harmonic oscillator with spring constant \( k \) and mass \( m \) is given by \( \omega = \sqrt{\frac{k}{m}} \). This formula determines how quickly the oscillator oscillates back and forth.
466. Which formula describes the relationship between the current \( I \) flowing through a conductor, the charge \( Q \) passing through it in time \( t \), and the number of charge carriers \( n \)?
ⓐ. \( I = \frac{Q}{n \cdot t} \)
ⓑ. \( I = \frac{n \cdot t}{Q} \)
ⓒ. \( I = Q \cdot n \cdot t \)
ⓓ. \( I = \frac{Q}{n + t} \)
Correct Answer: \( I = \frac{Q}{n \cdot t} \)
Explanation: The current \( I \) flowing through a conductor is related to the charge \( Q \) passing through it in time \( t \) and the number of charge carriers \( n \) by the formula \( I = \frac{Q}{n \cdot t} \).
467. What is the formula for the moment of inertia \( I \) of a thin rod of length \( L \) and mass \( M \) rotating about an axis perpendicular to its length and passing through its center?
ⓐ. \( I = \frac{1}{3}ML^2 \)
ⓑ. \( I = \frac{1}{2}ML^2 \)
ⓒ. \( I = \frac{ML^2}{12} \)
ⓓ. \( I = ML^2 \)
Correct Answer: \( I = \frac{ML^2}{12} \)
Explanation: The moment of inertia \( I \) of a thin rod of length \( L \) and mass \( M \) rotating about an axis perpendicular to its length and passing through its center is given by \( I = \frac{ML^2}{12} \).
468. Which formula represents the relationship between the electric field \( E \) between the plates of a parallel plate capacitor, the charge \( Q \) on the plates, and the distance \( d \) between them?
ⓐ. \( E = \frac{Q}{\epsilon_0 d} \)
ⓑ. \( E = Q \cdot \epsilon_0 \cdot d \)
ⓒ. \( E = \frac{Q}{\epsilon_0 + d} \)
ⓓ. \( E = Q + \epsilon_0 \cdot d \)
Correct Answer: \( E = \frac{Q}{\epsilon_0 d} \)
Explanation: The electric field \( E \) between the plates of a parallel plate capacitor is related to the charge \( Q \) on the plates and the distance \( d \) between them by \( E = \frac{Q}{\epsilon_0 d} \), where \( \epsilon_0 \) is the permittivity of free space.
469. What is the formula for the pressure \( P \) exerted by a gas in a container of volume \( V \) at temperature \( T \) and containing \( N \) moles of gas?
ⓐ. \( P = \frac{NRT}{V} \)
ⓑ. \( P = \frac{VRT}{N} \)
ⓒ. \( P = \frac{N}{VRT} \)
ⓓ. \( P = \frac{RT}{NV} \)
Correct Answer: \( P = \frac{NRT}{V} \)
Explanation: The pressure \( P \) exerted by a gas in a container of volume \( V \) at temperature \( T \) and containing \( N \) moles of gas is given by \( P = \frac{NRT}{V} \), where \( R \) is the universal gas constant.
470. Which formula describes the relationship between the force \( F \) exerted by an ideal spring with spring constant \( k \) and its displacement \( x \) from equilibrium?
ⓐ. \( F = kx \)
ⓑ. \( F = \frac{k}{x} \)
ⓒ. \( F = \frac{x}{k} \)
ⓓ. \( F = k + x \)
Correct Answer: \( F = kx \)
Explanation: The force \( F \) exerted by an ideal spring with spring constant \( k \) and displacement \( x \) from equilibrium is given by \( F = kx \).
471. What is the formula for the period \( T \) of a simple pendulum of length \( L \) oscillating with small amplitude?
ⓐ. \( T = 2\pi \sqrt{\frac{L}{g}} \)
ⓑ. \( T = 2\pi \sqrt{\frac{g}{L}} \)
ⓒ. \( T = \pi \sqrt{\frac{L}{g}} \)
ⓓ. \( T = \pi \sqrt{\frac{g}{L}} \)
Correct Answer: \( T = 2\pi \sqrt{\frac{L}{g}} \)
Explanation: The period \( T \) of a simple pendulum of length \( L \) oscillating with small amplitude is given by \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( g \) is the acceleration due to gravity.
472. Which formula represents the relationship between the work \( W \) done by a constant force \( F \) acting over a displacement \( d \) in the direction of the force?
ⓐ. \( W = Fd \)
ⓑ. \( W = \frac{F}{d} \)
ⓒ. \( W = \frac{d}{F} \)
ⓓ. \( W = F + d \)
Correct Answer: \( W = Fd \)
Explanation: The work \( W \) done by a constant force \( F \) acting over a displacement \( d \) in the direction of the force is given by \( W = Fd \).
473. What is the formula for the power \( P \) dissipated in an electrical resistor \( R \) carrying current \( I \)?
ⓐ. \( P = RI^2 \)
ⓑ. \( P = \frac{I}{R} \)
ⓒ. \( P = \frac{R}{I} \)
ⓓ. \( P = IR \)
Correct Answer: \( P = RI^2 \)
Explanation: The power \( P \) dissipated in an electrical resistor \( R \) carrying current \( I \) is given by \( P = RI^2 \).
474. Which formula describes the relationship between the force \( F \) required to accelerate an object of mass \( m \) with acceleration \( a \)?
ⓐ. \( F = ma \)
ⓑ. \( F = \frac{m}{a} \)
ⓒ. \( F = \frac{a}{m} \)
ⓓ. \( F = m + a \)
Correct Answer: \( F = ma \)
Explanation: The force \( F \) required to accelerate an object of mass \( m \) with acceleration \( a \) is given by \( F = ma \).
475. What is the formula for the period \( T \) of a mass-spring system with spring constant \( k \) and mass \( m \)?
ⓐ. \( T = 2\pi \sqrt{\frac{m}{k}} \)
ⓑ. \( T = \frac{2\pi}{\sqrt{km}} \)
ⓒ. \( T = \pi \sqrt{\frac{m}{k}} \)
ⓓ. \( T = \pi \sqrt{\frac{k}{m}} \)
Correct Answer: \( T = 2\pi \sqrt{\frac{m}{k}} \)
Explanation: The period \( T \) of a mass-spring system with spring constant \( k \) and mass \( m \) is given by \( T = 2\pi \sqrt{\frac{m}{k}} \).
476. Which formula represents the relationship between the wavelength \( \lambda \) of a wave, its frequency \( f \), and the wave speed \( v \)?
ⓐ. \( v = \lambda f \)
ⓑ. \( \lambda = \frac{v}{f} \)
ⓒ. \( f = \frac{v}{\lambda} \)
ⓓ. \( \lambda = vf \)
Correct Answer: \( v = \lambda f \)
Explanation: The wave speed \( v \) is related to the wavelength \( \lambda \) and frequency \( f \) by the formula \( v = \lambda f \).
477. What is the formula for the electric potential energy \( U \) of a point charge \( q \) in an electric field \( E \)?
ⓐ. \( U = qE \)
ⓑ. \( U = \frac{q}{E} \)
ⓒ. \( U = q \cdot E \)
ⓓ. \( U = E \cdot q \)
Correct Answer: \( U = E \cdot q \)
Explanation: The electric potential energy \( U \) of a point charge \( q \) in an electric field \( E \) is given by \( U = E \cdot q \).
478. Which formula describes the relationship between the force \( F \) exerted by an ideal gas, its pressure \( P \), and volume \( V \)?
ⓐ. \( F = \frac{PV}{T} \)
ⓑ. \( F = P \cdot V \)
ⓒ. \( F = \frac{P}{V} \)
ⓓ. \( F = PV \)
Correct Answer: \( F = PV \)
Explanation: The force \( F \) exerted by an ideal gas is related to its pressure \( P \) and volume \( V \) by the formula \( F = PV \).
479. What is the formula for the torque \( \tau \) produced by a force \( F \) acting at a perpendicular distance \( r \) from a pivot point?
ⓐ. \( \tau = Fr \)
ⓑ. \( \tau = \frac{F}{r} \)
ⓒ. \( \tau = \frac{r}{F} \)
ⓓ. \( \tau = F + r \)
Correct Answer: \( \tau = Fr \)
Explanation: The torque \( \tau \) produced by a force \( F \) acting at a perpendicular distance \( r \) from a pivot point is given by \( \tau = Fr \).
480. Which formula represents the relationship between the critical angle \( \theta_c \) for total internal reflection, refractive index \( n \) of the medium, and incident medium?
ⓐ. \( \sin \theta_c = \frac{1}{n} \)
ⓑ. \( \sin \theta_c = n \)
ⓒ. \( \cos \theta_c = \frac{1}{n} \)
ⓓ. \( \cos \theta_c = n \)
Correct Answer: \( \sin \theta_c = \frac{1}{n} \)
Explanation: The critical angle \( \theta_c \) for total internal reflection is related to the refractive index \( n \) of the medium and the incident medium by \( \sin \theta_c = \frac{1}{n} \).
481. What is the formula for the centripetal acceleration \( a_c \) of an object moving in a circle of radius \( r \) with constant speed \( v \)?
ⓐ. \( a_c = \frac{v^2}{r} \)
ⓑ. \( a_c = \frac{r}{v^2} \)
ⓒ. \( a_c = v \cdot r \)
ⓓ. \( a_c = r + v \)
Correct Answer: \( a_c = \frac{v^2}{r} \)
Explanation: The centripetal acceleration \( a_c \) of an object moving in a circle of radius \( r \) with constant speed \( v \) is given by \( a_c = \frac{v^2}{r} \).
482. Which formula describes the relationship between the focal length \( f \) of a lens, its refractive index \( n \), and the radius of curvature \( R \)?
ⓐ. \( f = \frac{n}{R} \)
ⓑ. \( f = \frac{R}{n} \)
ⓒ. \( f = \frac{n \cdot R}{2} \)
ⓓ. \( f = \frac{2 \cdot n \cdot R}{n – 1} \)
Correct Answer: \( f = \frac{R}{n} \)
Explanation: The focal length \( f \) of a lens is related to its refractive index \( n \) and the radius of curvature \( R \) by \( f = \frac{R}{n} \).
483. What is the formula for the period \( T \) of a simple harmonic oscillator with spring constant \( k \) and mass \( m \)?
ⓐ. \( T = 2\pi \sqrt{\frac{k}{m}} \)
ⓑ. \( T = \frac{2\pi}{\sqrt{km}} \)
ⓒ. \( T = \pi \sqrt{\frac{k}{m}} \)
ⓓ. \( T = \pi \sqrt{\frac{m}{k}} \)
Correct Answer: \( T = 2\pi \sqrt{\frac{m}{k}} \)
Explanation: The period \( T \) of a simple harmonic oscillator with spring constant \( k \) and mass \( m \) is given by \( T = 2\pi \sqrt{\frac{m}{k}} \).
484. Which formula represents the relationship between the heat \( Q \) absorbed or released during a phase change, the mass \( m \) of the substance, and the latent heat of fusion \( L_f \)?
ⓐ. \( Q = L_f \cdot m \)
ⓑ. \( Q = \frac{L_f}{m} \)
ⓒ. \( Q = \frac{m}{L_f} \)
ⓓ. \( Q = m + L_f \)
Correct Answer: \( Q = L_f \cdot m \)
Explanation: The heat \( Q \) absorbed or released during a phase change is related to the mass \( m \) of the substance and the latent heat of fusion \( L_f \) by \( Q = L_f \cdot m \).
485. What is the formula for the energy \( E \) stored in a capacitor with capacitance \( C \) and voltage \( V \)?
ⓐ. \( E = \frac{1}{2} CV^2 \)
ⓑ. \( E = \frac{1}{2} \frac{V}{C} \)
ⓒ. \( E = \frac{1}{2} CV \)
ⓓ. \( E = CV^2 \)
Correct Answer: \( E = \frac{1}{2} CV^2 \)
Explanation: The energy \( E \) stored in a capacitor with capacitance \( C \) and voltage \( V \) is given by \( E = \frac{1}{2} CV^2 \).
486. Which formula describes the relationship between the Doppler effect, the frequency \( f’ \) of the observed wave, the frequency \( f \) of the source, the speed of sound \( v \), and the relative velocity \( v_{rel} \)?
ⓐ. \( f’ = f \cdot \frac{v}{v + v_{rel}} \)
ⓑ. \( f’ = f \cdot \frac{v + v_{rel}}{v} \)
ⓒ. \( f’ = f \cdot \frac{v}{v – v_{rel}} \)
ⓓ. \( f’ = f \cdot \frac{v – v_{rel}}{v} \)
Correct Answer: \( f’ = f \cdot \frac{v + v_{rel}}{v} \)
Explanation: The frequency \( f’ \) of the observed wave due to the Doppler effect, when the source is moving with a relative velocity \( v_{rel} \), is given by \( f’ = f \cdot \frac{v + v_{rel}}{v} \).
487. What is the formula for the magnetic force \( F \) on a charge \( q \) moving with velocity \( v \) in a magnetic field \( B \)?
ⓐ. \( F = qvB \)
ⓑ. \( F = \frac{q}{vB} \)
ⓒ. \( F = \frac{vB}{q} \)
ⓓ. \( F = Bvq \)
Correct Answer: \( F = qvB \)
Explanation: The magnetic force \( F \) on a charge \( q \) moving with velocity \( v \) in a magnetic field \( B \) is given by \( F = qvB \).
488. Which formula represents the relationship between the angular velocity \( \omega \), linear velocity \( v \), and radius \( r \) of rotation?
ⓐ. \( \omega = \frac{v}{r} \)
ⓑ. \( v = \frac{\omega}{r} \)
ⓒ. \( \omega = vr \)
ⓓ. \( v = \omega \cdot r \)
Correct Answer: \( \omega = \frac{v}{r} \)
Explanation: The angular velocity \( \omega \) of an object rotating with linear velocity \( v \) at a radius \( r \) is given by \( \omega = \frac{v}{r} \).
489. What is the formula for the electric field \( E \) generated by a point charge \( Q \) at a distance \( r \) from the charge?
ⓐ. \( E = \frac{Q}{4 \pi \epsilon_0 r^2} \)
ⓑ. \( E = \frac{4 \pi \epsilon_0 Q}{r^2} \)
ⓒ. \( E = \frac{Q}{r^2} \)
ⓓ. \( E = \frac{r^2}{Q} \)
Correct Answer: \( E = \frac{Q}{4 \pi \epsilon_0 r^2} \)
Explanation: The electric field \( E \) generated by a point charge \( Q \) at a distance \( r \) from the charge is given by \( E = \frac{Q}{4 \pi \epsilon_0 r^2} \), where \( \epsilon_0 \) is the permittivity of free space.
490. Which formula describes the relationship between the buoyant force \( F_b \), density of the fluid \( \rho \), gravitational acceleration \( g \), and volume \( V \) of the displaced fluid?
ⓐ. \( F_b = \rho gV \)
ⓑ. \( F_b = \frac{\rho}{gV} \)
ⓒ. \( F_b = \frac{gV}{\rho} \)
ⓓ. \( F_b = \rho + g + V \)
Correct Answer: \( F_b = \rho gV \)
Explanation: The buoyant force \( F_b \) exerted on an object submerged in a fluid is given by \( F_b = \rho gV \), where \( \rho \) is the density of the fluid, \( g \) is the acceleration due to gravity, and \( V \) is the volume of the displaced fluid.
This is the final section of Class 11 Physics MCQs – Chapter 5: Laws of Motion (Part 5). The chapter as a whole consists of 490 multiple-choice questions with accurate answers and explanations, arranged into 5 parts for structured learning. Designed according to the NCERT/CBSE syllabus, these questions are essential for strong preparation in board exams and competitive exams such as JEE, NEET, and state-level entrance tests. Here in the last part, you will find 90 MCQs with detailed solutions to complete your practice for this chapter.
- 👉 This is Part 5 — final set of 90 MCQs with answers.
- 👉 Best for last-minute revision before board and competitive exams.
- 👉 To explore more chapters, subjects, or classes, simply use the top navigation bar.
- 👉 Completing all 5 parts covers the full set of 490 questions.