A smooth sphere of radius R is fixed on a horizontal surface. A steel ball, moving horizontally with velocity v0=5gR, collides with the sphere, changes its direction and moves with velocity v as shown. Then

Tangential speed is unchanged ⇒v0cos37°=vcos30°⇒v0×45=v × 32⇒8v0=53v

A smooth sphere of radius R is fixed on a horizontal surface. A steel ball, moving horizontally with velocity v0=5gR, collides with the sphere, changes its direction and moves with velocity v as shown. Then

Tangential speed is unchanged ⇒v0cos37°=vcos30°⇒v0×45=v × 32⇒8v0=53v

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A smooth sphere of radius $R$ is fixed on a horizontal surface. A steel ball, moving horizontally with velocity $v_{0} = 5 \sqrt{g R}$ , collides with the sphere, changes its direction and moves with velocity $v$ as shown. Then

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$4 \sqrt{2} v_{0} = 5 \sqrt{3} v$

$8 v_{0} = 5 \sqrt{3} v$

$5 v_{0} = 8 \sqrt{3} v$

$v = v_{0}$

answer is B.

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Detailed Solution

Tangential speed is unchanged $\Rightarrow v_{0} \cos 37 ° = v \cos 30 °$

$\Rightarrow v_{0} \times \frac{4}{5} = v \times \frac{\sqrt{3}}{2} \Rightarrow 8 v_{0} = 5 \sqrt{3} v$

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A smooth sphere of radius R is fixed on a horizontal surface. A steel ball, moving horizontally with velocity v0=5gR, collides with the sphere, changes its direction and moves with velocity v as shown. Then

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A smooth sphere of radius $R$ is fixed on a horizontal surface. A steel ball, moving horizontally with velocity $v_{0} = 5 \sqrt{g R}$ , collides with the sphere, changes its direction and moves with velocity $v$ as shown. Then