A sphere of radius R and having negligible mass is floating in a large lake. An external agent slowly pushes the sphere so as to submerge it completely. How much work was done by the agent? Density of water is `rho`.

A ring of mass m_(1) and radius R is fixed in space at some location. An external agent brings a point mass m_(2) from infinity to centre of the ring. Work done by the external agent will be

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If rlt ltR and the surface tension of water is T, value of r just before bubbles detach is: (density of water is rho_w )

A hollow sphere of external radius R and thickness t (< < R) is made of a metal of density rho . The sphere will float in water if

A sperical ball of radius r and relative density 0.5 is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is [ rho is the density of water]-

A metallic sphere of radius 21 cm is dropped into a cylindrical vessel, which is partly, filled with water. The diameter of the vessel is 1.68 m. If the sphere is completely submerged, find by how much the surface of water will rise.

On heating water, bubbles beings formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and amking a circular contact of radius r with the bottom of the vessel. If r ltlt R , and the surface tension of water is T , value of r just before bubles detatch is : (density of water is rho_(w))

A small mass m is moved slowly from the surface of the earth to a height h above the surface. The work done (by an external agent) in doing this is