Question

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

A. `(3)/(2)R`
B. `(2)/(3) R`
C. `(1)/(2) R`
D. `(1)/(3) R`

Answer 1

(b) Suppose body slips at point B

`mgcostheta=(mv^(2))/(R)[v=sqrt(2g(R-h))]`
gcostheta=(2g(R-h))/(R)`
`costheta=(2(R-h))/(R)`
`(h)/(R)=(2(R-h))/(R)" " [costheta=(h)/(R)]`
`:." "h=(2)/(3)R`