A is a fixed point at height H above a perfectly inelastic smooth horizontal plane. A light inextesnsible string of length `L(gtH)` has one end attached to A and other to a heavy particle. The particle is held at the level of A with string just taut and released from rest. Find the height of the particle above the plane when it is next instaneously at rest .

(i) O is a fixed peg at a height H above a perfectly inelastic smooth horizontal plane. A light inextensible string of length L (gt H) has one end attached to O and the other end is attached to a heavy particle. The particle is held at the level of O with string horizontal and just taut and released from rest. Find the height of the particle above the plane when it comes to rest for the first time after the release. (ii) The bob of a pendulum has mass m and the length of pendulum is l . It is initially at rest with the string vertical and the point of suspension at a height 2l above the floor. A particle P of mass (m)/(2) moving horizontally along –ve x-direction with velocity sqrt(2gl) collides with the bob and comes to rest. The bob swings and when it comes to rest for the first time, another particle Q of mass m moving horizontally along y direction collides with the bob and sticks to it. It is observed that the bob now moves in a horizontal circle. (a) Find tension in string just before the second collision. (b) Find the height of the circular path above the floor. (c) Find the time period of the circular motion. (d) The string breaks during the circular motion at time t = 0 . At what time the bob will hit the floor ?

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizontally with speed (gl) . Then the speed of the particle and the inclination of the string to the vertical at the instant of the motion when the tension in the string equal the weight of the particle-

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizontally with speed (gl) . Then the speed of the particle and the inclination of the string to the vertical at the instant of the motion when the tension in the string equal the weight of the particle-

A light rigid rod of length l is hinged at one end and it is free to rotate in a vertical plane. A particle of mass m is attached to another end of the rod. The particle is released from rest at its highest point. Select the correct statement out of the following

A heavy particle hanging from a string of length l is projected horizontally with speed sqrtgl . Find the speed of the particle at the point where the tension in the string equals weight of the particle.

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizonally with speed sqrt(gl) . Find the speed of the particle and the inclination of the string to the vertical at the instant of the motion when the tension in the string is equal to the weight of the particle.

A heavy particle hanging from a fixed point by a light inextensible string of length l is projected horizonally with speed sqrt(gl) . Find the speed of the particle and the inclination of the string to the vertical at the instant of the motion when the tension in the string is equal to the weight of the particle.

A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle about the point C

A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle about the point C