A particle of mass m is placed on top of a smooth hemispherical wedge of mass 4m at rest. The hemispherical wedge is kept on a frictionless horizontal surface. The particle is given a gentle push. The angular velocity of the particle relative to the wedge if wedge has velocity v when particle has fallen an angle $θ$ with respect to the wedge is

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$\frac{5 v}{Rcosθ}$

$\frac{v}{Rcosθ}$

$\frac{4 v}{Rcosθ}$

answer is A.

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Detailed Solution

Applying conservation of momentum of the system along horizontal direction

$- 4 mv + m (v_{1} cosθ - v) = 0$

$v_{1} = \frac{5 v}{\cos θ}$

$where v_{1} = velocity of particle with respect to hemisphere and ω = \frac{v_{1}}{R}$

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