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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

160237_f511490a8edb4b32b90cdac60fdfb900.png


A
1:1
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B
2:1
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C
8:3
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D
11:8
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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 $$K.E_p : K.E_s= 8 : 3$$

445627_160237_ans_9b0edfac7f624448a9e4f79596f0704d.png

Physics

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