A small body of mass m slides down from the top of a hemisphere or radius r (Fig$$. $$2). The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

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Infinity Learn · Accepted Answer

See fig. (8). The body will lose contact when centripetal acceleration becomes equal to the component of acceleration due to gravity along the radius.Velocity at P,       $$v=2g(r$$−$$h)$$∵        $$v2$$−$$u2=2gxCentripetal$$ acceleration will be $$v2/r$$. It should be equal to the component of g along PO. $$Hencev2r=gcos$$⁡θor             $$2g(r$$−$$h)r=g$$×hrSolving, we get $$h=2r3$$

A small body of mass m slides down from the top of a hemisphere or radius r (Fig. 2). The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

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