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501. Which type of friction is responsible for initiating rolling motion of a body on a surface?
ⓐ. Kinetic friction
ⓑ. Static friction
ⓒ. Rolling friction
ⓓ. Viscous friction
Correct Answer: Static friction
Explanation: Rolling motion begins because of static friction, which prevents slipping and provides the torque needed for rotation. Kinetic friction only acts when there is slipping.
502. When a solid sphere rolls without slipping on a horizontal surface, the work done by friction is:
ⓐ. Positive
ⓑ. Negative
ⓒ. Zero
ⓓ. Maximum
Correct Answer: Zero
Explanation: In pure rolling, static friction does no work because the point of contact has no relative displacement with respect to the surface.
503. A uniform solid cylinder of mass \(M\) and radius \(R\) is pulled by a force \(F\) at its center. For rolling without slipping, the friction force acts:
ⓐ. Forward
ⓑ. Backward
ⓒ. Upward
ⓓ. Zero
Correct Answer: Backward
Explanation: The applied force tends to slide the cylinder, so static friction acts backward to provide the torque necessary for rolling.
504. The torque responsible for rolling motion without slipping is produced by:
ⓐ. Gravitational force
ⓑ. Normal reaction
ⓒ. Frictional force
ⓓ. Centripetal force
Correct Answer: Frictional force
Explanation: Frictional force at the point of contact provides the torque that causes rotational acceleration during rolling.
505. For a body rolling without slipping, the condition linking linear acceleration \(a\) and angular acceleration \(\alpha\) is:
ⓐ. \(a = \tau/I\)
ⓑ. \(a = \omega r\)
ⓒ. \(a = \alpha r\)
ⓓ. \(a = F/m\)
Correct Answer: \(a = \alpha r\)
Explanation: The relationship between linear and angular accelerations for rolling without slipping is \(a = \alpha r\).
506. The acceleration of the center of mass of a rolling cylinder on an inclined plane of angle \(\theta\) is:
ⓐ. \(g \sin\theta\)
ⓑ. \(\frac{g \sin\theta}{2}\)
ⓒ. \(\frac{2g \sin\theta}{3}\)
ⓓ. \(\frac{g \cos\theta}{2}\)
Correct Answer: \(\frac{2g \sin\theta}{3}\)
Explanation: Using Newton’s second law and torque balance, the acceleration for a solid cylinder is \(a = \frac{g \sin\theta}{1 + (I/MR^2)} = \frac{2g \sin\theta}{3}\).
507. For a rolling object, which statement about friction is correct?
ⓐ. Friction always opposes rolling
ⓑ. Friction always accelerates rolling
ⓒ. Friction can either oppose or support rolling depending on external forces
ⓓ. Friction is unnecessary for rolling motion
Correct Answer: Friction can either oppose or support rolling depending on external forces
Explanation: Friction may act forward or backward depending on whether the body is rolling down an incline, pulled, or pushed. It only ensures no slipping occurs.
508. A solid sphere of mass \(M\) rolls down an incline of angle \(\theta\). The force of static friction acts:
ⓐ. Up the incline
ⓑ. Down the incline
ⓒ. Zero
ⓓ. Perpendicular to incline
Correct Answer: Up the incline
Explanation: Static friction acts up the incline to prevent slipping and provide the torque necessary for rotation.
509. When a wheel rolls without slipping, the mechanical energy of the system is:
ⓐ. Only translational kinetic energy
ⓑ. Only rotational kinetic energy
ⓒ. Sum of translational and rotational kinetic energy
ⓓ. Constantly decreasing due to friction
Correct Answer: Sum of translational and rotational kinetic energy
Explanation: In rolling motion, total energy is shared between translational KE \(\tfrac{1}{2} M v^2\) and rotational KE \(\tfrac{1}{2} I \omega^2\).
510. If friction is suddenly removed while a body is rolling on a horizontal surface, it will:
ⓐ. Stop immediately
ⓑ. Continue pure rolling indefinitely
ⓒ. Slide while gradually reducing rotation
ⓓ. Continue rolling with slipping
Correct Answer: Continue rolling with slipping
Explanation: Without friction, no torque acts to maintain rolling condition. Thus the body continues with its existing translational and rotational velocities, but slipping occurs as \(v \neq \omega r\).
511. The total kinetic energy of a body rolling without slipping is given by:
ⓐ. \(\tfrac{1}{2} M v^2\)
ⓑ. \(\tfrac{1}{2} I \omega^2\)
ⓒ. \(\tfrac{1}{2} M v^2 + \tfrac{1}{2} I \omega^2\)
ⓓ. \(M g h\)
Correct Answer: \(\tfrac{1}{2} M v^2 + \tfrac{1}{2} I \omega^2\)
Explanation: The kinetic energy in rolling motion is the sum of translational KE of the center of mass and rotational KE about the center of mass. Both parts are essential to describe the energy distribution in rolling.
512. For a rolling sphere, if translational kinetic energy is \(T\), then rotational kinetic energy is:
ⓐ. Equal to \(T\)
ⓑ. Less than \(T\)
ⓒ. Greater than \(T\)
ⓓ. Zero
Correct Answer: Less than \(T\)
Explanation: For a solid sphere, \(I = \tfrac{2}{5}MR^2\). The rotational KE = \(\tfrac{1}{2} I \omega^2 = \tfrac{1}{5} M v^2\), while translational KE = \(\tfrac{1}{2} M v^2\). Hence rotational KE is smaller.
513. Which rolling body reaches the bottom of an incline first (assuming no slipping)?
ⓐ. Solid sphere
ⓑ. Solid cylinder
ⓒ. Hollow sphere
ⓓ. Thin ring
Correct Answer: Solid sphere
Explanation: Acceleration on incline is \(a = \tfrac{g \sin\theta}{1 + I/(MR^2)}\). The smaller \(I/(MR^2)\), the faster the acceleration. For a solid sphere, \(I/(MR^2) = 2/5\), which is the least among the given options.
514. The loss in potential energy when a rolling body descends a height \(h\) is equal to:
ⓐ. Only translational KE gained
ⓑ. Only rotational KE gained
ⓒ. Sum of translational and rotational KE gained
ⓓ. Always zero
Correct Answer: Sum of translational and rotational KE gained
Explanation: In absence of non-conservative forces, the decrease in gravitational potential energy is converted into both translational and rotational kinetic energies of the body.
515. For a uniform ring rolling without slipping, the ratio of translational KE to rotational KE is:
ⓐ. 1:1
ⓑ. 2:1
ⓒ. 1:2
ⓓ. 3:2
Correct Answer: 1:1
Explanation: For a ring, \(I = MR^2\). Rotational KE = \(\tfrac{1}{2} I \omega^2 = \tfrac{1}{2} MR^2 (\tfrac{v}{R})^2 = \tfrac{1}{2} M v^2\), which is equal to translational KE.
516. Which factor determines the distribution of energy between translational and rotational motion in rolling?
ⓐ. Radius of the body
ⓑ. Mass of the body
ⓒ. Shape and moment of inertia of the body
ⓓ. Acceleration due to gravity
Correct Answer: Shape and moment of inertia of the body
Explanation: The ratio of rotational KE to translational KE depends on \(I/MR^2\), which varies with the shape of the rolling object, not just its mass or size.
517. When a rolling object moves on a horizontal surface without external forces, its total kinetic energy is:
ⓐ. Constant
ⓑ. Increasing
ⓒ. Decreasing
ⓓ. Zero
Correct Answer: Constant
Explanation: In absence of external forces or friction doing work, both translational and rotational kinetic energies remain constant, so total KE stays constant.
518. In rolling without slipping, the fraction of total energy in rotational form for a solid cylinder is:
ⓐ. \(\tfrac{1}{2}\)
ⓑ. \(\tfrac{1}{3}\)
ⓒ. \(\tfrac{1}{4}\)
ⓓ. \(\tfrac{2}{3}\)
Correct Answer: \(\tfrac{1}{3}\)
Explanation: For a solid cylinder, \(I = \tfrac{1}{2}MR^2\). Rotational KE = \(\tfrac{1}{2} I \omega^2 = \tfrac{1}{4} M v^2\). Total KE = \(\tfrac{3}{4} M v^2\). Hence rotational fraction = \(\tfrac{1}{4}/\tfrac{3}{4} = 1/3\).
519. A solid sphere and a hollow sphere of equal mass and radius roll down the same incline. Which has greater rotational KE at the bottom?
ⓐ. Solid sphere
ⓑ. Hollow sphere
ⓒ. Both equal
ⓓ. Depends on incline length
Correct Answer: Hollow sphere
Explanation: For the same mass and radius, the hollow sphere has a larger moment of inertia, so a greater portion of gravitational potential energy is converted into rotational KE.
520. Which statement is correct about energy considerations in rolling motion?
ⓐ. Rotational KE is always more than translational KE
ⓑ. Translational KE is always more than rotational KE
ⓒ. Distribution depends on the shape and \(I/MR^2\) ratio
ⓓ. Rotational KE is independent of shape
Correct Answer: Distribution depends on the shape and \(I/MR^2\) ratio
Explanation: The division of potential energy into rotational and translational parts depends only on the geometry and moment of inertia ratio of the rolling object.
521. Why are wheels preferred in vehicles instead of sliding blocks?
ⓐ. Wheels reduce normal force
ⓑ. Wheels eliminate the need for friction
ⓒ. Wheels reduce energy loss due to friction
ⓓ. Wheels increase mass of vehicle
Correct Answer: Wheels reduce energy loss due to friction
Explanation: Wheels allow rolling motion, where static friction ensures no relative sliding at the contact point. This minimizes energy loss compared to sliding motion, making vehicles more efficient.
522. Which of the following demonstrates rolling motion in everyday life?
ⓐ. A block pushed across a rough floor
ⓑ. A ball rolling on the ground
ⓒ. A book sliding off a table
ⓓ. A parachute falling vertically
Correct Answer: A ball rolling on the ground
Explanation: Rolling motion occurs when a body rotates while also translating, as seen in a ball rolling, where the condition \(v = \omega r\) holds true.
523. Why is it easier to roll a heavy cylinder up an incline than to slide it?
ⓐ. Because rolling reduces gravitational force
ⓑ. Because rolling reduces the effective acceleration by distributing energy
ⓒ. Because cylinders are hollow
ⓓ. Because rolling eliminates torque
Correct Answer: Because rolling reduces the effective acceleration by distributing energy
Explanation: In rolling, some potential energy converts into rotational KE, lowering net acceleration and making it easier compared to sliding, which faces full kinetic friction.
524. What ensures the smooth rolling of railway train wheels on tracks?
ⓐ. Kinetic friction
ⓑ. Static friction
ⓒ. Air resistance
ⓓ. Normal reaction
Correct Answer: Static friction
Explanation: Static friction prevents slipping between the wheel and track, allowing efficient rolling motion and safe train operation.
525. Which factor makes rolling motion of car tires more energy efficient?
ⓐ. Large weight of the car
ⓑ. Reduced contact area of wheels
ⓒ. Rolling friction is much smaller than sliding friction
ⓓ. Use of hollow wheels
Correct Answer: Rolling friction is much smaller than sliding friction
Explanation: Rolling friction is minimal compared to sliding friction, which ensures lower energy loss and smooth, efficient driving.
526. Which of the following is an application of rolling motion in daily life?
ⓐ. Using ball bearings in machinery
ⓑ. Using ropes in pulleys
ⓒ. Free fall of an object
ⓓ. Heat transfer in metals
Correct Answer: Using ball bearings in machinery
Explanation: Ball bearings convert sliding motion into rolling motion, reducing friction and wear in machines, thereby increasing efficiency and durability.
527. Why do heavy trucks use more tires?
ⓐ. To increase sliding friction
ⓑ. To increase rolling resistance
ⓒ. To distribute load and reduce pressure per wheel
ⓓ. To make the vehicle heavier
Correct Answer: To distribute load and reduce pressure per wheel
Explanation: More tires distribute the vehicle’s weight, reducing rolling resistance and minimizing damage to roads while maintaining stability.
528. Why does a solid sphere reach the bottom of an incline faster than a hollow sphere?
ⓐ. It has less radius
ⓑ. It has smaller moment of inertia
ⓒ. It has greater static friction
ⓓ. It has greater mass
Correct Answer: It has smaller moment of inertia
Explanation: A solid sphere has \(I = \tfrac{2}{5}MR^2\), while a hollow sphere has \(I = MR^2\). The smaller inertia of the solid sphere means more energy goes into translational motion, increasing acceleration.
529. Why do bicycles and motorcycles have wheels with thin tires?
ⓐ. To reduce rotational inertia and rolling resistance
ⓑ. To increase the vehicle’s weight
ⓒ. To increase sliding friction
ⓓ. To reduce normal force
Correct Answer: To reduce rotational inertia and rolling resistance
Explanation: Thin tires reduce moment of inertia and contact surface, making rolling easier and requiring less torque for motion, improving speed and efficiency.
530. What is the main function of rolling motion in conveyor belt rollers?
ⓐ. To increase friction
ⓑ. To reduce friction and facilitate smooth transfer of loads
ⓒ. To stop motion completely
ⓓ. To increase gravitational force on objects
Correct Answer: To reduce friction and facilitate smooth transfer of loads
Explanation: Conveyor belt rollers use rolling motion to minimize resistance, allowing goods to move smoothly and efficiently with minimal energy consumption.
531. Why are cylindrical rollers used in road construction?
ⓐ. To increase sliding friction on the road
ⓑ. To apply uniform pressure and compact the surface through rolling
ⓒ. To reduce the weight of the vehicle
ⓓ. To make the road uneven
Correct Answer: To apply uniform pressure and compact the surface through rolling
Explanation: Heavy cylindrical rollers use rolling motion to distribute force uniformly, pressing down loose particles and compacting road surfaces efficiently without excessive friction losses.
532. What is the role of rolling motion in ballpoint pens?
ⓐ. To increase writing resistance
ⓑ. To allow smooth ink transfer onto paper
ⓒ. To prevent the pen from drying
ⓓ. To increase friction between pen and paper
Correct Answer: To allow smooth ink transfer onto paper
Explanation: The ball at the tip of a ballpoint pen rolls while writing, ensuring continuous transfer of ink and reducing wear by minimizing sliding friction.
533. How do bowling balls demonstrate rolling motion?
ⓐ. They slide without rotating
ⓑ. They roll with both translational and rotational motion on the lane
ⓒ. They spin in place without translation
ⓓ. They only move because of kinetic friction
Correct Answer: They roll with both translational and rotational motion on the lane
Explanation: A bowling ball combines linear motion down the lane with rotation about its axis, demonstrating rolling motion as long as slipping is absent.
534. Why are rollers used in old printing presses?
ⓐ. To increase ink viscosity
ⓑ. To convert sliding into rolling and spread ink evenly
ⓒ. To increase the weight of the machine
ⓓ. To stop ink spreading
Correct Answer: To convert sliding into rolling and spread ink evenly
Explanation: Rollers in printing machines spread ink uniformly across paper using rolling motion, avoiding energy loss due to sliding friction.
535. In which of the following devices does rolling motion play a crucial role in reducing wear and tear?
ⓐ. Electric heaters
ⓑ. Ball bearings in fans
ⓒ. Solar panels
ⓓ. Light bulbs
Correct Answer: Ball bearings in fans
Explanation: Ball bearings convert sliding motion into rolling motion, drastically reducing friction and wear, thereby enhancing the lifespan of rotating machinery like fans.
536. Why do trains experience less resistance despite their massive weight?
ⓐ. Because wheels are lubricated with oil
ⓑ. Because of rolling motion on steel tracks with minimal rolling friction
ⓒ. Because of air resistance reduction
ⓓ. Because of large normal force
Correct Answer: Because of rolling motion on steel tracks with minimal rolling friction
Explanation: Train wheels use rolling motion over smooth steel rails, where rolling friction is extremely small, enabling efficient motion even for heavy loads.
537. Which of the following is an application of rolling motion in sports?
ⓐ. A football bouncing vertically
ⓑ. A cricket ball moving on the ground after being hit
ⓒ. A shuttlecock flying in air
ⓓ. A swimmer pushing water backward
Correct Answer: A cricket ball moving on the ground after being hit
Explanation: After being struck, the cricket ball rolls on the ground, demonstrating rolling motion where both translational velocity and angular velocity are linked.
538. Why are rollers used in textile industries?
ⓐ. To create more sliding friction for fabrics
ⓑ. To press and move fabrics smoothly through machines
ⓒ. To make fabrics heavier
ⓓ. To reduce tension in threads
Correct Answer: To press and move fabrics smoothly through machines
Explanation: Cylindrical rollers in textile machines use rolling motion to pull and press fabrics evenly, avoiding wear that would result from sliding friction.
539. Which of the following is an example of rolling motion reducing energy consumption?
ⓐ. Dragging a suitcase without wheels
ⓑ. Pulling a sled on snow
ⓒ. Using a suitcase with wheels
ⓓ. Sliding a box across a floor
Correct Answer: Using a suitcase with wheels
Explanation: Suitcase wheels use rolling motion, minimizing resistance compared to sliding, thus making transport easier and energy-efficient.
540. Why do log rollers help in moving heavy wooden logs?
ⓐ. They increase sliding friction between logs and ground
ⓑ. They act as rolling supports, reducing resistance
ⓒ. They make the logs lighter in weight
ⓓ. They prevent torque generation
Correct Answer: They act as rolling supports, reducing resistance
Explanation: When logs are placed on cylindrical rollers, rolling motion reduces sliding resistance, making it easier to transport heavy wooden logs with minimal effort.
541. What is the radius of gyration of a body?
ⓐ. Distance of the axis from the center of mass
ⓑ. Equivalent distance from the axis at which the whole mass of the body is assumed to be concentrated to give the same moment of inertia
ⓒ. The radius of a sphere equivalent to the body
ⓓ. Distance from center to surface
Correct Answer: Equivalent distance from the axis at which the whole mass of the body is assumed to be concentrated to give the same moment of inertia
Explanation: Radius of gyration \(k\) is defined such that \(I = Mk^2\). It provides a simplified representation of how mass is distributed relative to the axis of rotation.
542. For a thin uniform rod of length \(L\) rotating about an axis passing through its center and perpendicular to its length, the radius of gyration is:
ⓐ. \(\frac{L}{\sqrt{3}}\)
ⓑ. \(\frac{L}{\sqrt{12}}\)
ⓒ. \(\frac{L}{2}\)
ⓓ. \(\frac{L}{\sqrt{2}}\)
Correct Answer: \(\frac{L}{\sqrt{12}}\)
Explanation: The moment of inertia is \(I = \frac{1}{12}ML^2\). Hence \(k = \sqrt{I/M} = \sqrt{L^2/12} = L/\sqrt{12}\).
543. The SI unit of radius of gyration is:
ⓐ. kg
ⓑ. m
ⓒ. rad
ⓓ. kg·m²
Correct Answer: m
Explanation: Since radius of gyration represents a length (distance equivalent), its SI unit is meter.
544. If two bodies have the same mass and same moment of inertia, which one has a smaller radius of gyration?
ⓐ. The one with mass farther from axis
ⓑ. The one with mass closer to axis
ⓒ. Both same
ⓓ. Depends on velocity
Correct Answer: The one with mass closer to axis
Explanation: Since \(I = Mk^2\), for same I and M, smaller k means mass distribution is closer to the axis.
545. The kinetic energy of a rotating rigid body can be expressed as:
ⓐ. \(KE = \frac{1}{2}I\omega^2\)
ⓑ. \(KE = \frac{1}{2}mv^2\)
ⓒ. \(KE = \frac{1}{2}mr^2\)
ⓓ. \(KE = I\omega\)
Correct Answer: \(KE = \frac{1}{2}I\omega^2\)
Explanation: The work-energy theorem for rotation shows that the rotational kinetic energy depends on the moment of inertia and square of angular velocity.
546. Which of the following correctly shows the analogy between translational and rotational motion?
ⓐ. Mass ↔ Torque
ⓑ. Force ↔ Angular Momentum
ⓒ. Mass ↔ Moment of Inertia
ⓓ. Linear velocity ↔ Angular Acceleration
Correct Answer: Mass ↔ Moment of Inertia
Explanation: In the analogy, inertia in linear motion is represented by mass, while in rotation it is represented by moment of inertia.
547. In rolling without slipping, the total kinetic energy of a body is:
ⓐ. Only translational KE
ⓑ. Only rotational KE
ⓒ. Sum of translational and rotational KE
ⓓ. Constant but always rotational
Correct Answer: Sum of translational and rotational KE
Explanation: A rolling body has both translational KE \(\frac{1}{2}Mv^2\) and rotational KE \(\frac{1}{2}I\omega^2\).
548. Which energy distribution makes a body accelerate faster down an incline?
ⓐ. Larger rotational KE
ⓑ. Smaller moment of inertia, hence more translational KE
ⓒ. Equal rotational and translational KE
ⓓ. Energy independent of inertia
Correct Answer: Smaller moment of inertia, hence more translational KE
Explanation: Bodies with smaller moments of inertia (e.g., solid sphere) have more energy in translational motion and reach the bottom faster.
549. Why does rolling motion waste less energy compared to sliding?
ⓐ. Because kinetic energy is zero in rolling
ⓑ. Because static friction involved in rolling does no work
ⓒ. Because rolling occurs only on smooth surfaces
ⓓ. Because angular velocity cancels linear velocity
Correct Answer: Because static friction involved in rolling does no work
Explanation: In rolling without slipping, the point of contact has no relative motion with the surface, so static friction does not cause energy loss.
550. Which type of friction is smaller:
ⓐ. Sliding friction
ⓑ. Rolling friction
ⓒ. Both same
ⓓ. Depends on surface only
Correct Answer: Rolling friction
Explanation: Rolling friction is much smaller than sliding friction, which is why wheels and ball bearings are widely used to reduce energy loss.
551. Which of the following is the correct analogy?
ⓐ. Force ↔ Torque
ⓑ. Momentum ↔ Angular velocity
ⓒ. Kinetic energy ↔ Angular momentum
ⓓ. Work ↔ Angular displacement
Correct Answer: Force ↔ Torque
Explanation: Torque is the rotational analogue of force, both producing acceleration in their respective motions.
552. An ice skater spins faster when she pulls in her arms. This is due to:
ⓐ. Conservation of linear momentum
ⓑ. Conservation of angular momentum
ⓒ. Increase in moment of inertia
ⓓ. Decrease in angular velocity
Correct Answer: Conservation of angular momentum
Explanation: As the skater pulls arms inward, her moment of inertia decreases, so angular velocity increases to conserve angular momentum.
553. Which astrophysical phenomenon is explained by conservation of angular momentum?
ⓐ. Expansion of the universe
ⓑ. Collapse of a rotating star into a neutron star
ⓒ. Blackbody radiation
ⓓ. Motion of planets due to gravity
Correct Answer: Collapse of a rotating star into a neutron star
Explanation: As the radius of the star decreases, its moment of inertia decreases. To conserve angular momentum, angular velocity increases, causing rapid spin.
554. Why do divers tuck their legs and arms while spinning?
ⓐ. To reduce gravitational pull
ⓑ. To reduce air resistance
ⓒ. To reduce moment of inertia and spin faster
ⓓ. To increase torque
Correct Answer: To reduce moment of inertia and spin faster
Explanation: Pulling limbs close to the axis reduces the moment of inertia, and angular velocity increases as angular momentum is conserved.
555. Which of the following is NOT an example of conservation of angular momentum?
ⓐ. A planet revolving around the Sun
ⓑ. A skater spinning faster by pulling in arms
ⓒ. A bullet hitting a wall and stopping
ⓓ. A collapsing star spinning faster
Correct Answer: A bullet hitting a wall and stopping
Explanation: In this case, external torque from the wall acts, so angular momentum is not conserved.
556. The expression for radius of gyration in terms of moment of inertia \(I\) and mass \(M\) is:
ⓐ. \(k = \frac{I}{M}\)
ⓑ. \(k = \sqrt{\frac{I}{M}}\)
ⓒ. \(k = \frac{M}{I}\)
ⓓ. \(k = \sqrt{IM}\)
Correct Answer: \(k = \sqrt{\frac{I}{M}}\)
Explanation: By definition, \(I = Mk^2\), hence \(k = \sqrt{I/M}\).
557. A solid cylinder and a hollow cylinder of same mass and radius roll down an incline. Which reaches first?
ⓐ. Both together
ⓑ. Solid cylinder
ⓒ. Hollow cylinder
ⓓ. Depends on surface
Correct Answer: Solid cylinder
Explanation: Solid cylinder has smaller moment of inertia, so it has more translational acceleration and reaches earlier.
558. In the analogy between linear and rotational motion, angular displacement corresponds to:
ⓐ. Velocity
ⓑ. Force
ⓒ. Linear displacement
ⓓ. Energy
Correct Answer: Linear displacement
Explanation: Angular displacement is the rotational analogue of linear displacement in straight-line motion.
559. What determines the rotational inertia of a body?
ⓐ. Its velocity
ⓑ. Its shape and mass distribution relative to axis
ⓒ. Its kinetic energy
ⓓ. Its gravitational force
Correct Answer: Its shape and mass distribution relative to axis
Explanation: The farther the mass is distributed from the axis, the greater the moment of inertia.
560. Which device uses rolling motion to minimize energy losses in machines?
ⓐ. Springs
ⓑ. Ball bearings
ⓒ. Fans
ⓓ. Capacitors
Correct Answer: Ball bearings
Explanation: Ball bearings replace sliding contact with rolling contact, greatly reducing energy loss due to friction.
561. The parallel axis theorem is useful for calculating:
ⓐ. Torque on a rotating body
ⓑ. Moment of inertia about any axis parallel to an axis through center of mass
ⓒ. Angular momentum of a body
ⓓ. Kinetic energy of rotation
Correct Answer: Moment of inertia about any axis parallel to an axis through center of mass
Explanation: The theorem states \(I = I_{cm} + Md^2\), where \(d\) is the distance between axes.
562. The perpendicular axis theorem applies to:
ⓐ. Any rigid body
ⓑ. Only 3D bodies
ⓒ. Only 2D planar laminae
ⓓ. Fluids
Correct Answer: Only 2D planar laminae
Explanation: The theorem states \(I_z = I_x + I_y\) and is valid for planar laminae only.
563. Which physical quantity is conserved when no external torque acts on a system?
ⓐ. Linear momentum
ⓑ. Angular momentum
ⓒ. Work
ⓓ. Kinetic energy
Correct Answer: Angular momentum
Explanation: Absence of external torque ensures conservation of angular momentum, analogous to linear momentum conservation without external force.
564. Which factor makes rolling motion preferable in transport systems?
ⓐ. Larger torque generation
ⓑ. Smaller rolling friction compared to sliding friction
ⓒ. Zero energy loss
ⓓ. Increase in inertia
Correct Answer: Smaller rolling friction compared to sliding friction
Explanation: Rolling reduces resistance, making motion smoother and more energy-efficient compared to sliding.
565. Which of the following analogies is correct?
ⓐ. Linear momentum ↔ Angular displacement
ⓑ. Force ↔ Torque
ⓒ. Work ↔ Angular momentum
ⓓ. Mass ↔ Angular velocity
Correct Answer: Force ↔ Torque
Explanation: Torque in rotational motion corresponds to force in translational motion.
566. In which case is angular momentum NOT conserved?
ⓐ. A freely spinning top in vacuum
ⓑ. A skater pulling arms inward
ⓒ. A cyclist pedaling on frictionless surface
ⓓ. A wheel slowed down by brake pads
Correct Answer: A wheel slowed down by brake pads
Explanation: Brake pads exert external torque, so angular momentum is not conserved.
567. The expression for rotational KE using radius of gyration \(k\) is:
ⓐ. \(\frac{1}{2}Mv^2\)
ⓑ. \(\frac{1}{2}Mk^2\omega^2\)
ⓒ. \(Mk\omega\)
ⓓ. \(\frac{1}{2}M\omega^2\)
Correct Answer: \(\frac{1}{2}Mk^2\omega^2\)
Explanation: Since \(I = Mk^2\), rotational KE becomes \(\frac{1}{2}I\omega^2 = \frac{1}{2}Mk^2\omega^2\).
568. Which real-life example demonstrates conservation of angular momentum in space?
ⓐ. Satellite in orbit changing speed by firing thrusters
ⓑ. A planet orbiting sun
ⓒ. An astronaut spinning and then curling into a ball
ⓓ. A falling apple from tree
Correct Answer: An astronaut spinning and then curling into a ball
Explanation: In absence of external torque in space, the astronaut reduces moment of inertia, causing an increase in angular velocity.
569. When a gymnast stretches arms sideways during spin, the rotation:
ⓐ. Speeds up
ⓑ. Slows down
ⓒ. Stops
ⓓ. Remains same
Correct Answer: Slows down
Explanation: Stretching arms increases moment of inertia, decreasing angular velocity to conserve angular momentum.
570. Which physical law is common to both linear and rotational dynamics?
ⓐ. Newton’s first law only
ⓑ. Newton’s second law
ⓒ. Law of gravitation
ⓓ. Law of thermodynamics
Correct Answer: Newton’s second law
Explanation: In linear motion, \(F = ma\). In rotational motion, \(\tau = I\alpha\). Both describe acceleration under external influence.
This is the final part of Class 11 Physics MCQs – Chapter 7: System of Particles and Rotational Motion (Part 6). The complete chapter includes a total of 570 MCQs with detailed answers, divided into 6 structured parts for effective practice. Following the NCERT/CBSE syllabus, these questions are perfect for revising concepts for board exams as well as competitive exams like JEE, NEET, and state-level entrance tests. On this page, you will find the final 70 MCQs with solutions, designed for quick revision and last-minute preparation. 🎉 Congratulations on completing this chapter! Now you can continue your preparation by exploring MCQs from other chapters using the top navigation bar.
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