A particle is given a negligible push from the top of a smooth fixed solid hemisphere of radius 15 m . It slides down the surface and eventually loses contact with it. The speed of the particle at the exact moment it loses contact with the hemisphere is: (Take g = 10 m/s ^2 )

Step-by-step solution

Let the particle lose contact with the hemisphere at an angle with the vertical. At this position, the forces acting along the radial direction are the component of gravity mg towards the center and the normal reaction N away from the center. The net radial force provides the necessary centripetal acceleration: mg - N = mv^2 R The condition for the particle to lose contact is N = 0 . Therefore: mg = mv^2 R v^2 = gR Now, applying conservation of mechanical energy from the top of the hemisphere to this point. The ver