1)

A solid cylinder of mass m and radius R rolls down the inclined plane without slipping. The speed of its C.M. when it reaches the bottom is

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A) 2gh

B) 4gh3

C) 34gh

D) 4gh

Answer:

Option B

Explanation:

By energy conservation

(K.E)+ (P.E)i = (K.E)f+ (P.E)f

(K.E)i =0,(P.E)i = mgh, (P.E)f = 0

 (K.E)= 12Iω2+12mv2

For the solid cylinder, the moment of inertia,

I = 12mR2

So, mgh =

12(12mR2)(v2R2)+12mv2

v = 4gh3