Q.

STATEMENT-1:
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously  allowed to roll without slipping down an inclined plane from the Same height. The hollow cylinder will reach the bottom of the
Inclined plane first.

STATEMENT-2:
By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the Bottom of the incline.
 

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a

Statement-1 is True; Statement-2 is True; Statement-2 is a correct explanation for Statement-1

b

Statement-1 is True; Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

c

Statement-1 is True, Statement-2 is False

d

Statement-1 is False; Statement-2 is True.

answer is D.

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Detailed Solution

By conservation of energy , we have  12mvc2+12Icω2=mgh

Question Image

Moment of inertia of solid and hollow cylinders are given as
Isolid=MR22​​     Ihollow=MR2
For pure rolling , we have 
ω=vcR      As   Isolid<Ihollow       vsolid>vhollow
Hence solid cylinder will reach the bottom first.
 

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