A block of mass m slides down along the
surface of the bowl of radiusr from the rim to
the bottom. The velocity of the block at the
bottom will be
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Applying work kinetic energy theorem on the block for the time interval t=0 to t=tₒ, Here h is the vertical height between the initial and final horizontal levels of the particle. If the bowl is hemispherical then obviously h=R; the radius of hemisphere and v=√(2gR).
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