First slide

Rolling motion

Question

A solid sphere of radius R is rolled by a force F acting at the top of the sphere as shown in the figure. There is no slipping and initially sphere is in the rest position then :

A) Work done by force F when the centre of mass moves a distance S is 2FS.
B) Speed of the CM when CM moves a distance S is $\large \sqrt {\frac{20}7\frac {FS}M}$
C) Work done by the force F when CM moves a distance S is FS
D) Speed of the CM when CM moves a distance S is $\large \sqrt {\frac {4FS}M$

Difficult

A

Only A & B are correct
B

only A & C are correct
C

only B & C are correct
D

only C & D are correct

Solution

If displacement of centre C of the sphere is S, the displacement of the topmost point A will be 2S. work done by force of friction is zero. By work-energy Theorem, $\large F.2S=\frac 12Mv^2+\frac 12\left ( \frac 25MR^2 \right )\left ( \frac vR \right )^2$
$\large \Rightarrow v=\sqrt {\frac {20FS}{7M}}$
Therefore statements (A) and (B) are correct.

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