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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 the materials of second sphere and first sphere is

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answer is C.

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Detailed Solution

For the first sphere,

$Density = ρ_{1} & volume = \frac{4}{3} {πr}^{3} = V$

For the second sphere,

$Density = ρ_{2} & volume = \frac{4}{3} {πr}^{3} / 8 = \frac{V}{8}$

From the conservation of linear momentum,

$ρ_{1} Vu = (ρ_{2} V / 8) u + 0$

$ρ_{2} = 8 ρ_{1}$

Hence the correct answer is 8.

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