JEE Advanced 2021 · Paper 1 · Physics Q11

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PhysicsMultiple correct+4 / -2Question 11 of 57

A horizontal force $F$ is applied at the center of mass of a cylindrical object of mass $m$ and radius $R$ , perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $\mu$ . The center of mass of the object has an acceleration $a$ . The acceleration due to gravity is $g$ . Given that the object rolls without slipping, which of the following statement(s) is(are) correct?

A cylinder (circle of radius R, radius drawn dashed) resting on horizontal ground, with a horizontal force F applied at its centre, pointing to the right.

For the same

F

, the value of

a

does not depend on whether the cylinder is solid or hollow

For a solid cylinder, the maximum possible value of

a

2\mu g

The magnitude of the frictional force on the object due to the ground is always

\mu mg

For a thin-walled hollow cylinder,

a = \dfrac{F}{2m}

Answer and worked solution

Official answer: B, D

Rolling equations. For rolling without slipping, with friction $f$ opposing the motion:
$F-f=ma,\qquad fR=I\frac aR\implies a=\frac{F}{m+I/R^2},\qquad f=\frac{I}{R^2}a.$

Check each option.

(A) $a$ depends on $I$ , which differs for solid and hollow cylinders. False.
(B) For a solid cylinder $I=\frac12mR^2$ , so $f=\frac{ma}2$ . Requiring $f\le\mu mg$ gives $a\le2\mu g$ . True.
(C) Static friction only takes whatever value is needed; it is not always $\mu mg$ . False.
(D) For a thin-walled cylinder $I=mR^2$ , so $a=\frac F{2m}$ . True.

(B), (D)

Topics:Rolling motion Friction Torque and rotational dynamics

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JEE Advanced 2021 · Paper 1, Physics question 11