A particle slides down from the top outside smooth surface of a fixed sphere of radius a=10m . The initial horizontal velocity to be imparted to the particle at the top is 5Km/s ,if it leaves the surface at a point whose vertical height above the centre of sphere is 3a/4. Find the value of K

A partcle rests on the top of a hemisphere of radius R. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down :

A particle of mass m slides down from the vertex of semi- hemisphere, without any initial velocity. At what height from horizontal will the particle leave the sphere-

A heavy particle of mass m is in motion on a smooth surface of hemisphere of radius R and there is no friction. At the initial instant the particle is at the topmost point A and has an initial velocity v_(0) At what point will the particle leave the surface of the hemisphere ? Also determine the value of v_(0) for which the particle will leave the sphere at the initial instant.

A small particle rest on the top of a hemisphere of radius 20 cm .The smallest horizontal velocity os given to it , if it is to leave the hemisphere without sliding down to its surface ,is

A particle of mass m starts to slide down from the top of the fixed smooth sphere. What is the tangential acceleration when it break off the sphere ?

A particle rests on the top of a smooth hemisphere of radius r . It is imparted a horizontal velocity of sqrt(etagr) . Find the angle made by the radius vector joining the particle with the vertical at the instant the particle losses contact with the sphere.

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

A very small particle rests on the top of a hemisphere of radius 20 cm . Calculate the smallest horizontal velocity to be given to it if it is to leave the hemisphere without sliding down its surface, take g = 9.8 m//s^(2) .