Question

Velocity of the centre of a small cylinder is $v$. There is no slipping anywhere. the velocity of the centre of the larger cylinder is

• A. $2v$
• B. $v$
• C. $\frac{3v}{2}$
• D. none of these

Answer 1

The correct option is B $v$

As there is no slipping, thus velocity of point C must be zero.

Thus $v-Rw=0⟹v=Rw$

Hence, $v_A=v+Rw=2v$

Similarly, velocity of point D must be zero.

Let $v^{\prime }$ be the velocity of center of larger cylinder.

Thus, $v^{\prime }-2Rw=0⟹v^{\prime }=2R{w}^{\prime }$ ..........(1)

$v_B=v_A=2v$

$v^{\prime }+2R{w}^{\prime }=2v$

From (1), $v^{\prime }=v$