First slide

Rolling motion

Question

A solid sphere and a solid cylinder of same mass are rolled down on two inclined planes of heights h₁ and h₂, respectively. If at the bottom of the plane, the two objects have same linear velocities, then the ratio of h₁ : h₂ is

Moderate

A

2 : 3
B

7: 5
C

14 : 15
D

15: 14

Solution

According to the question,
${(K_{T})}_{sphere} = {(K_{T})}_{cylinder}$ (m and v are same)
$∴ \frac{5}{7} (m g h_{1}) = \frac{2}{3} (m g h_{2})$
$\Rightarrow \frac{h_{1}}{h_{2}} = \frac{14}{15}$

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