A circular ring of mass M and radius R is placed in YZ plane with centre at origin. A particle of mass m is released from rest at a point x = 2R. Find the speed with which it will pass the centre of ring .

The gravitational force vec(F) upon an object of mass m placed in external gravitational field vec(E )_("ext") is given by vec(F)=m vec(E )_("ext") . Consider a fixed mass ring (of mass M, radius R) in y-z plane, with centre at (0,0) and axis of ring along x direction. If the particle (mass m) is released from rest from a point distant x = R sqrt(3) , then it will pass through the centre of ring with speed

A point P(Rsqrt(3),0,0) lies on the axis of ring of mass M and radius R the ring is located in YZ plane with its centre at origin O A small particle of mass m starts from P and reaches O under gravitatinal attracton only its speed at O will be

A ring with a uniform charge Q and radius R , is placed in the yz plane with its centre at the origin

A point P(R sqrt(3),0,0) lies on the axis of a ring of mass M and radius R. The ring is located in yx-plane with its centre at origin O. A small particle of mass m starts from P and reaches O under gravitational attraction only. Its speed at O will be

A point P (Rsqrt(3)m,0,) lies on the axis of a ring of mass M and radius R. The ring is located in y -z plane with its centre at origin. A small particle of mass m start from P and reaches O under gravitational attraction only. Its speed at O will be.

A circular ring of mass M and radius 'a' is placed in a gravity free space. A small particle of mass m placed on the axis of the ring at a distance sqrt(3)a from the center of the ring, is released from rest. The velocity with which the particle passes through the center of the ring is

For a uniform ring of mass M and radius R at its centre

A circular ring of mass m and radius R rests flat on a horizontal smooth surface as shown in figure. A particle of mass m , and moving with a velocity v . Collides inelastically (e=0) with the ring the angular velocity with which the system rotates after the particle strikes the ring is

Consider two identical rings of mass M and radius R fixed on a horizontal axis in a gravity - free space. A particle of mass m is held at rest at the centre of 1^("st") ring and projected along the axis towards 2^("nd") ring. The minimum speed of projection so that the particle reaches the centre of 2^("nd") ring is