Assertion (A): It is more difficult to open the door by applying the force near the hinge.
Reason (R): Torque is maximum at hinge.
Assertion (A) is true: Torque \(\tau = rF\sin\theta\) requires a larger force \(F\) for a smaller lever arm \(r\) (near the hinge). Reason (R) is false: Torque is zero at the hinge (pivot point) as \(r=0\). Thus, (A) is true, (R) is false.
Assertion (A): Angular momentum of a body may remain conserved even when moment of inertia of body changes.
Reason (R): Angular momentum of a body does not depend upon moment of inertia of the body.
Assertion (A) is true: If no external torque acts, angular momentum \(L\) is conserved. If moment of inertia \(I\) changes, angular velocity \(\omega\) adjusts to keep \(L = I\omega\) constant.
Reason (R) is false: Angular momentum \(L = I\omega\) explicitly depends on the moment of inertia \(I\). Thus, (A) is true, (R) is false.
Assertion (A): In case of rolling without sliding, friction force can act in forward and backward direction both.
Reason (R): The angular momentum of a system will be conserved only about that point about which external angular impulse is zero.
Assertion (A) is true: Friction acts to prevent slipping, which can be forward or backward depending on the situation (e.g., accelerating or braking).
Reason (R) is true: Angular momentum is conserved when the net external torque (and thus angular impulse) about the point is zero. Both statements are true, but R does not explain A.
Assertion (A): A body is rolling without slipping on a surface. There must be frictional force to start such a motion.
Reason (R): In rolling without slipping, work done against the frictional force is zero on rolling body.
Assertion (A) is true: Friction provides the necessary torque to initiate the angular acceleration required for rolling.
Reason (R) is true: In pure rolling, the point of contact is instantaneously at rest, so the work done by static friction is zero. Both statements are true, but R does not explain A.