IIT JEE Problem: A ball is held in the position shown with string of length 1m just taut and then projected horizontally with speed 3m/s

A metal bob of mass 0.6 kg is attached to the end of a string of length 1 m and the bob is whirled in a horizontal circle with a uniform speed of 12 m/s. What is the centripetal force acting on the bob ? If the speed of the bob is 5 m/s calculate the tension in the string.

A particle is suspended by a light vertical inelastic string of length 1 from a fixed support. At its equilbrium position it is projected horizontally with a speed sqrt(6 g l) . Find the ratio of the tension in the string in its horizontal position to that in the string when the particle is vertically above the point of support.

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 equal mass m are attached by a string of length 2l and initially placed over a smooth horizontal table in the position shown in fig. particle B is projected across the table with speed u perpendicular to AB as shown in the figure. find the velocities of each particle after the string becomes taut and the magnitude of the impulse tension.

A ball of mass 1kg is attached to an inextensible string. The ball is released from the position shown in figure. Find the impulse imparted by the string to the ball immediately after the string becomes taut. (Take g=10m//s^2 )

A stone hanging from a massless string of length 15m is projected horizontally with speed sqrt(147) ms^(-1) Then the Speed of the particle, at the point where tension in string equals the weight of particle, is

A stone hanging from a massless string of length 15 m is projected horizontally with speed 12ms^(-1) . The speed of the particle at the point where the tension in the string is equal to the weight of the particle, is close to

One end of a light string of length L is connected to a ball and the other end is connected to a fixed point O . The ball is released from rest at t = 0 with string horizontal and just taut. The ball then moves in vertical circular path as shown. The time taken by ball to go from position A to B is t_(1) and from B to lowest position C is t_(2) . Let the velocity of ball at B is vec v_(B) and at C is vec v_(C) respectively. If |vec v_(C)=2|vecv_(B)| then the value of theta as shown is

A ball with mass m is attached to the end of a rod of mass M and length l . The other end of the rod is pivoted so that the ball can move in a vartical circle. The rod is held in the horizontal position as shown in figure and then given just enough a downward push so that the ball swings down and just reaches the vertical upward position having zero speed there. Now answer the following questions. The initial speed given to the ball is

A ball with mass m is attached to the end of a rod of mass M and length l . The other end of the rod is pivoted so that the ball can move in a vartical circle. The rod is held in the horizontal position as shown in figure and then given just enough a downward push so that the ball swings down and just reaches the vertical upward position having zero speed there. Now answer the following questions. The change in potential energy of the system (ball+rod) is