IIT-JEE 2012 · Paper 2 · Physics Q18

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PhysicsMultiple correct+4Question 18 of 60

Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface, while $Q$ has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

Both cylinders

P

and

Q

reach the ground at the same time.

Cylinder

P

has larger linear acceleration than cylinder

Q

Both cylinders reach the ground with same translational kinetic energy.

Cylinder

Q

reaches the ground with larger angular speed.

Answer and worked solution

Official answer: D

Rolling down an incline. $a=\dfrac{g\sin\theta}{1+I/(mR^2)}$ . P (mass near the rim) has the larger $I$ , so the smaller acceleration.

(A) Q has the larger acceleration and arrives first. False.
(B) P has the smaller acceleration. False.
(C) Both lose the same potential energy, but P puts more of it into rotation, so its translational kinetic energy is smaller. False.
(D) Q reaches the bottom with the larger speed $v$ , so the larger $\omega=v/R$ . True.

(D)

Topics:Rolling motion Moment of inertia

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IIT-JEE 2012 · Paper 2, Physics question 18