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Rotational Inertia

A solid spher...

Question

A solid sphere is moving and it makes an elastic collision with another stationary sphere of half of its own radius. After collision it comes to rest. The ratio of the densities of materials of second sphere and first sphere is-

A

2

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B

4

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C

8

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D

16

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Solution

The correct option is C $8$
For $1^{s t}$ sphere
Density= $ρ_{1}$
Volume= $\frac{4}{3} π r^{3} = V$
For $2^{n d}$ sphere
Density= $ρ_{2}$
Volume= $\frac{4}{3} π r^{3} / 8 = V / 8$
From Conservation of Linear Momentum
$ρ_{1} V u = ρ_{2} V / 8 u + 0$
$⟹ ρ_{2} = 8 ρ_{1}$

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