A particle slides on surface of a fixed smooth sphere starting from topmost point. The angle rotated by the radius through the particle, when it leaves contact with the sphere, is

Step-by-step solution

See the diagram Let the velocity be v when the body leaves the surface. From free body diagram, m v^2 R =m g . v^2=R g ...(i) Again from work energy principle, change in KE = work done 1 2 m v^2-0=m g[R-R ]v^2=2 g R(1- ) ...(ii) From Eqs. (i) and (ii) aligned R g & =2 g R(1- ) 3 g R & =2 g R & = 2 3 = ⁻¹ ( 2 3 ) aligned