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Q.

A hollow hemispherical bowl of mass m, radius R is placed on a smooth horizontal surface. A particle (also of mass m) strikes the hemi spherical bowl at point P and sticks to it. The velocity of particle just after the  collision in vertically upwards direction is ku25;where k is an integer. Find k.
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answer is 3.

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Detailed Solution

Vy=ωxcosθ=ωR2
Using conservation of angular momentum about centre of mass.
muR4=23mR2mR24+5mR216ω+5mR216ω=2524mR2ωω=6u25RVy=3u25
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