Question

A plank P is placed on a solid cylinder S, which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of kinetic energy of P to the kinetic energy of S is

• A. $1:1$
• B. $2:1$
• C. $8:3$
• D. $11:8$

Answer 1

The correct option is C $8:3$

As there is no slipping at A and B i.e $v=Rw$

Also $v_p=v+Rw=2v$

$K.E_p=\frac{1}{2}m{v}_p^2=2m{v}^2$

$K.E_s=\frac{1}{2}I{w}^2+\frac{1}{2}m{v}^2$

$K.E_s=\frac{1}{2}\times \frac{1}{2}m{R}^2{w}^2+\frac{1}{2}m{v}^2$

$K.E_s=\frac{3}{4}m{v}^2$ (as v=Rw)

Thus $K.E_p:K.E_s=8:3$