A small sphere of mass m and radius r slides | vedclass

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(A) Since the surface of the bowl is smooth, there is no friction to cause the sphere to roll. The sphere will simply slide down the surface.By the la

Vedclass · Accepted Answer

$mg(R-r)$

Vedclass · Answer

(A) Since the surface of the bowl is smooth, there is no friction to cause the sphere to roll. The sphere will simply slide down the surface.By the law of conservation of mechanical energy, the loss in potential energy is equal to the gain in kinetic energy.The change in height of the center of mass of the sphere is $h = R - r$.Potential energy lost = $mgh = mg(R - r)$.Since the sphere is sliding (not rolling), its total kinetic energy is purely translational: $K = \frac{1}{2} mv^2$.Therefore, the total kinetic energy at the lowest point is $K = mg(R - r)$.

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