A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod moves transitionally in the vertical plane with an accleration `a_(0)` in direction forming angle `alpha` with the rod as shown. The acceleration of bead with respect to rod is:
`z`

A bead of mass m moves on a rod without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration a_(0) in a direction forming angle theta with the horizontal as shown in the given figure. The acceleration of bead with respect to rod is

A ring of radius R lies in vertical plane. A bead of mass 'm' can move along the ring without friction. Initially the bead is at rest the bottom most point on ring. The minimum horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle.

A ring of radius R lies in vertical plane. A bead of mass 'm' can move along the ring without friction. Initially the bead is at rest the bottom most point on ring. The minimum horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle.

A ring of radius R lies in vertical plane. A bead of mass 'm' can move along the ring without friction. Initially the bead is at rest the bottom most point on ring. The minimum horizontal speed v with which the ring must be pulled such that the bead completes the vertical circle.

A rod of mass 'm and length L is attached to a L shaped plank at 'A'. rod can move freely about A. A string is tied between rod and plank as shown in figure. Whole system is moving with a constant acceleration g in x-direction If string is cut at any instant then the angular acceleration of rod (with respect to the plank) at that instant is

A rod touches a disc kept on a smooth horizontal plane. If the rod moves with an acceleration a , the disc rolls on the rod without acceleration a , the disc rools on therod without slidding. Then , the acceleration of the disc w.r.t the rod is

A smooth uniform rod of length L and mass M has two identical beads of negligible size each of mass m which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with an angular velocity omega_0 about an axis perpendicular to the rod and passing through the midpoint of the rod. There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is ......