Assertion (A): When the disc rolls without slipping, friction is required because condition of pure rolling is velocity of point of contact is zero.
Reason (R): The force of friction in the case of a disc rolling without slipping down an inclined plane is zero.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: For pure rolling, the point of contact velocity is zero, and friction provides the necessary torque.
Reason (R) is false: For a disc rolling without slipping down an inclined plane, friction is present and acts up the incline to provide the torque for rotation. Thus, (A) is true, (R) is false.
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.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
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.
Assertion (A): A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling).
Reason (R): For pure rolling, work done against frictional force is zero.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true; friction provides the torque for rolling. Without friction, the wheel slips. Reason (R) is true; in pure rolling, the contact point is stationary, so static friction does no work. However, (R) does not explain (A).
A solid sphere of radius R is placed in smooth horizontal surface. A horizontal force F is applied, at height ‘h’ from the lowest point. For the maximum acceleration of centre of mass, which is correct:
(2002)
1. h = R
2. h = 2R
3. h = 0
4. No relation between h and R
View Answer
Acceleration of the centre of mass is given by $a = frac{F}{m} + frac{tau}{I}R_{text{eff}}$. For a smooth surface with no friction, force torque about centre is $tau = F(h-R)$. Maximizing acceleration depends on applying force at the top point where $h = 2R$ to maximize translational effect without opposing torque constraints, or simply using Newton's second law where $a = F/m$ is independent of $h$ unless specified with rotation, but for rolling/sliding conditions $h=2R$ yields specific torque relations.
A disc is rolling the velocity of its centre of mass is $v_{\text{cm}}$ then which one will be correct:
(2001)
1. The velocity of highest point is $2 v_{\text{cm}}$ and point of contact is zero
2. The velocity of highest point is $v_{\text{cm}}$ and point of contact is $v_{\text{cm}}$
3. The velocity of highest point is $2 v_{\text{cm}}$ and point of contact is $v_{\text{cm}}$
4. The velocity of highest point is $2 v_{\text{cm}}$ and point of contact is $2 v_{\text{cm}}$
View Answer
For pure rolling, the velocity of the topmost point is $$v*{\text{cm}} + \omega R = 2v_{\text{cm}}$$ and the point of contact is $$v_{\text{cm}} - \omega R = 0$$.