A particle `P` of mass `m` is attached by a light inextensible string of length `2a` to a fixed point `O`. When vertically below O,P is given a horizontal velocity `u` as shown figure (i) . When `OP` beocmes horizontal the string hits a small smooth nail. `Q` distant a from `O` and the particle continues to rotats about `Q` as center as shown figure (ii). The particle just describes complete circle about the nail. The value of `(u^(2))/(ga)` is

Acceleration-velocity graph of a moving particle is shown in figure. The particle is

A particle of mass 2m is connected by an inextensible string of length 1.2 m to a ring of mass m which is free to slide on a horizontal smooth rod. Initially the ring and the particle are at the same level with the string taut. Both are then released simultaneously. The distance in meter moved by the ring when the string becomes veritcal is :-

A particle P of mass m is attached to a vertical axis by two strings AP and BP of length l each. The separation AB=l. P rotates around the axis with an angular velocity omega . The tensions in the two strings are T_(1) and T_(2)

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in figure. The horizontal velocity of the block is :

A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown figure . What will be the trajectory of the particle , if the string is cut at (a) point B ? (b) point C ? (C ) Point X ?

Two particles each of mass m are connected by a light inextensible string and a particle of mass M is attached to the midpoint of the string. The system is at rest on a smooth horizontal table with string just taut and in a straight line. The particle M is given a velocity v along the table perpendicular to the string. Prove that when the two particles are about to collide : (i) The velocity of M is (Mv)/((M + 2m)) (ii) The speed of each of the other particles is ((sqrt2M (M + m))/((M + 2m)))v .

Two particles A and B of mass 2m and m respectively are attached to the ends of a light inextensible string of length 4a which passes over a small smooth peg at a height 3a from an inelastic table. The system is released from rest with each particle at a height a from the table. Find - (i) The speed of B when A strikes the table (ii) The time that elapses begore A first hits the table. (iii) The time for which A is resting on the table after the first collision & begore it is first jerked off.

A point mass m is suspended from a light thread of length l, fixed at O, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are

A particle is projected with a velocity 10 m/s at an angle 37^(@) to the horizontal. Find the location at which the particle is at a height 1 m from point of projection.

A particle is subjected to a force which varies with distance as shown in figure . The work done on the particle at in dispalcement of 12 m is …… . .