From a solid sphere of radius R a quarter of sphere is cut out. The center of mass of remaining part is at a distance `frac{sqrt2R} {N}` from centre of sphere .Find the value of N.

From a circular disc of radius R, a square is cut out with a radius as its diagonal. The center of mass of remaining portion is at a distance from the center)

From a circular disc of radius R, a square is cut out with a radius as its diagonal. The center of mass of remaining portion is at a distance from the center)

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The center of the ring is at a distance sqrt3 a from the center of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

Figure shows a uniformly charged sphere of radius R and total charge Q. A point charge q is situated outside the sphere at a distance r from centre of sphere. Find out the following : (i) Force acting on the point charge q due to the sphere. (ii) Force acting on the sphere due to the point charge.

A uniform solid sphere of radius R has a cavity of radius 1m cut from it if centre of mass of the system lies at the periphery of the cavity then

A uniform solid sphere of radius R has a cavity of radius 1m cut from it if centre of mass of the system lies at the periphery of the cavity then

A spherical cave of radius R/2 was carved out from a uniform sphere of radius R and original mass M. the center of the cave is at R/2 from the center of the large sphere. Point P is at a distance 2R from the center the large sphere and on the joing line of the two centers. the gravitational field strength g at point P is

A conducting sphere of radius R is charged to a potential of V volts. Then the electric field at a distance r ( gt R) from the centre of the sphere would be