A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R.At what height will the ball lose contact with surface of the sphere?

A rubber ball of mass 10 g and radius 2 cm is submerged in water up to a depth of 5 cm and released. Find the height up to which the ball pops up above the surface of water, neglecting the resistance of water and air. The density of water = 1g*cm^(-3) .

A ball dropped from a height of 10 m rebounds from the floor and rises to a height of 2.5 m. If the ball spends 0.01 s in contact with the floor then find out the average acceleration during that contact.

A small sphere of radius r at rest begins to slide down the surface of a hemispherical bowl from the brim of the bowl. When the sphere reaches the bottom of the bowl, what fraction of its total energy will be converted into translational kinetic energy and what fraction into rotational kinetic energy ?

A path ball of mass 1g carrying an electric charge of 980 esu is dropped on a charged sphere of radius 10 cm from a height of 1m above the centre of the latter. It is found that the pith ball momentarily comes to rest on the charged sphere before being repelled away again. Calculate the charge on the sphere.