A solid cylinder and a solid sphere, having the same mass M and radius R, roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be

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(4) √(14)/(15). Rolling without slipping from rest through a height h: Mgh=1/2Mv²(1+k) with k=I/(MR²), so v²=(2gh)/(1+k). Solid cylinder, k=1/2: v_c²=(2gh)/(3/2)=(4gh)/3. Solid sphere, k=2/5: vₛ²=(2gh)/(7/5)=(10gh)/7. (v_c²)/(vₛ²)=4/3·7/(10)=(28)/(30)=(14)/(15). (v_c)/(vₛ)=√(14)/(15). The mass and the radius cancel, so the answer would be the same for a marble and a barrel.

A solid cylinder and a solid sphere, having the same mass M and radius R, roll down the same inclined plane from the top without slipping. They start from rest. The ratio of the velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be

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Why the other options are wrong