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

Solution

## The correct option is C $$8:3$$As there is no slipping at A and B  i.e  $$v= Rw$$Also $$v_p= v + Rw= 2v$$$$K.E_p= \dfrac{1}{2}mv_p^2= 2mv^2$$$$K.E_s= \dfrac{1}{2}Iw^2 + \dfrac{1}{2}mv^2$$$$K.E_s= \dfrac{1}{2}\times \dfrac{1}{2}mR^2w^2 + \dfrac{1}{2}mv^2$$$$K.E_s= \dfrac{3}{4}mv^2$$            (as v=Rw)Thus $$K.E_p : K.E_s= 8 : 3$$Physics

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