Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.
Q.1. Assertion : The centre of mass of a body may lie where there is no mass.
Reason : Centre of mass of body is a point, where the whole mass of the body is supposed to be concentrated.
AnswerAnswer: (a) As the concept of centre of mass is only theoretical, therefore in practice no mass may lie at the centre of mass. For example, centre of mass of a uniform circular ring is at the centre of the ring where there is no mass.
Q.2. Assertion : The earth is slowing down and as a result the moon is coming nearer to it.
Reason : The angular momentum of the earth moon system is conserved.
AnswerAnswer:(d) The earth is not slowing down. The angular momentum of the earth – moon system is conserved.
Q.3. Assertion : When you lean behind over the hind legs of the chair, the chair falls back after a certain angle.
Reason : Centre of mass lying outside the system makes the system unstable.
Q.4. Assertion : The centre of mass of system of n particles is the weighted average of the position vector of the n particles making up the system.
Reason : The position of the centre of mass of a system in independent of coordinate system.
Q.5. Assertion: Centre of mass of a ring lies at its geometric centre though there is no mass.
Reason: Centre of mass is independent of mass.
Q.6. Assertion : The centre of mass of an isolated system has a constant velocity.
Reason : If centre of mass of an isolated system is already at rest, it remains at rest.
Q.7. Assertion : The position of centre of mass of body depend upon shape and size of the body.
Reason : Centre of mass of a body lies always at the centre of the body
AnswerAnswer: (c) The position of centre of mass of a body depends on shape, size and distribution of mass of the body. The centre of mass does not lie necessarily at the centre of the body.
Q.8. Assertion : If no external force acts on a system of particles, then the centre of mass will not move in any
Reason : If net external force is zero, then the linear momentum of the system remains constant.
Q.9. Assertion : A particle is moving on a straight line with a uniform velocity, its angular momentum is always zero.
Reason : The momentum is not zero when particle moves with a uniform velocity.
Q.10. Assertion : The centre of mass of a two particle system lies on the line joining the two particle, being closer to the heavier particle.
Reason : Product of mass of particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.
Q.11. Assertion : For a system of particles under central force field, the total angular momentum is conserved.
Reason : The torque acting on such a system is zero.
AnswerAnswer: (a) Both the assertion and reason are true.
Q.12. Assertion: Torque is a vector quantity directed opposite to the applied force.
Reason: Torque τ=- r x F
Q.13. Assertion : It is harder to open and shut the door if we apply force near the hinge.
Reason : Torque is maximum at hinge of the door.
AnswerAnswer: (c) Torque = Force × perpendicular distance of line of action of force from the axis of rotation (d).
Hence for a given applied force, torque or true tendency of rotation will be high for large value of d. If distance d is smaller, then greater force is required to cause the same torque, hence it is harder to open or shut down the door by applying a force near the hinge.
Q.14. Assertion : Torque is equal to rate of change of angular momentum.
Reason : Angular momentum depends on moment of inertia and angular velocity.
Q.15. Assertion: When no external torque acts on a body, its angular velocity remains constant as long as moment of inertia is constant.
Reason: Torque τ = 0; dL/dt = 0, L = constant. L = Iω = constant
Q.16. Assertion: When axis of rotation passes through the centre of gravity, then the moment of inertia of a rigid body increases.
Reason: At the centre of gravity mass gets concentrated and moment of inertia increases.
AnswerAnswer: (d) The moment of inertia of a rigid body reduces to its minimum value, when the axis of rotation passes through its centre of gravity because the weight of a rigid body always acts through its centre of gravity.
Q.17. Assertion: An ice-skater stretches out arms-legs during performance.
Reason: Stretching out arms-legs helps the performer to balance his or her body so that he or she does not fall.
AnswerAnswer: (c) An ice-skater stretches out arms and legs during performance to take advantage of principle of conservation of angular momentum. As on doing so, their moment of inertia increases or decreases respectively and hence the angular velocity of spin motion decreases or increases accordingly.
Q.18. Assertion : If polar ice melts, days will be longer.
Reason : Moment of inertia decreases and thus angular velocity increases.
AnswerAnswer: (c) As the polar ice melts, water so formed flows towards the equator. The moment of inertia of the earth increases. To conserve angular momentum, angular velocity decreases. This increases the length (T = 2π/ω) of the day.
Q.19. Assertion : The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.
Reason : For all solid bodies total kinetic energy is always twice the translational kinetic energy.
Q.20. Assertion : Moment of inertia of a particle is same, whatever be the axis of rotation
Reason : Moment of inertia depends on mass and distance of the particles.
AnswerAnswer: (d) The moment of inertia of a particle about an axis of rotation is given by the product of the mass of the particle and the square of the perpendicular distance of the particle from the axis of rotation. For different axis, distance would be different, therefore moment of inertia of a particle changes with the change in axis of rotation
Q.21. Assertion : Radius of gyration of body is a constant quantity.
Reason : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particle from the axis of rotation.
Q.22. Assertion: A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of lowest point on the disc is zero.
Reason : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocity of the lowest point on the disc is always zero.
AnswerAnswer: (d) For a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of lowest point of disc is directed vertically upwards and is not zero (Due to translation part of rolling, acceleration of lowest point is zero. Due to rotational part of rolling, the tangential acceleration of lowest point is zero and centripetal acceleration is non-zero and upwards). Hence assertion is false.
Q.23. Assertion : When a sphere is rolls on a horizontal table it slows down and eventually stops.
Reason : When the sphere rolls on the table, both the sphere and the surface deform near the contact. As a result, the normal force does not pass through the centre and provide an angular declaration.
Q.24. Assertion : The velocity of a body at the bottom of an inclined plane of given height, is more when it slides down the plane, compared to when it is rolling down the same plane.
Reason : In rolling, down, a body acquires both, kinetic energy of translation and rotation.
AnswerAnswer: (a) In sliding down, the entire potential energy is converted into kinetic energy. While in rolling down some part of potential energy is converted into K.E. of rotation. Therefore linear velocity acquired is less.
Q.25. Assertion : A wheel moving down a frictionless inclined plane will slip and not roll on the plane.
Reason : It is the frictional force which provides a torque necessary for a body to roll on a surface.