A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is…

Question

A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30^ , then the angle of inclination of plane B must be (approximately)

Accepted Answer

Correct answer: C. (c) For a rolling body on inclined plane, a= mg sin ⁡ m+ IR^2= g sin ⁡ 1+ I mR ∵ Distance covered by body , s= 12at^2 ∵S_ sphere =S_ cylinder 12a_ sphere t^2= 12 a_ cylinder t^2 ⇒a_ sphere =a_ cylinder ⇒ g sin ⁡30^ 1+ 25mR^2mR^2= g sin ⁡ 1+ mR^2mR^2 ⇒ 12 75= sin ⁡ 2 ⇒ sin ⁡ = 57 ⇒ = sin^-1 ⁡ ( 57 )=45.6^ ≈45^

$A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30^{\circ}, then the angle of inclination of plane B must be (approximately)$

Solution

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