A mass m rotating freely in a horizontal circle of a radius 1m on a frictionless smooth table support a stationary mass 2m, attached to the other end of the string passing through smooth hole O in table, hanging vertically. Find the angular velocity of rotation.

two masses 2m and m are attached to the the ends of a string while passing over a smooth Pulley of mass m and radius R . The ratio of tensions in both the strings is

A metal wire of negligible mass, length 1 m and cross-sectional area 10^(-6) m^(2) is kept on a smooth horizontal table with one end fixed on the table. A ball of mass 2kg is attached to the other end of the wire. When the wire and the ball are rotated with angular velocity of 20 rad/s, it is found that the wire is elongated by 10^(-3)m . If the Young's modulus of the metal is n xx 10^(11) N//m^(2) , then the value of n is

A puck is moving in a circle in a circle of radius r_(0) with a constant speed v_(0) on a level frictionless table. A string is attached to the punk, which holds it in the circle, the string passes through a frictionless hole and is attached on the other end to a hanging object of mass M. The puck is mow made to move with a speed v' = 3v_(0) , but still in circle. The mass of the hanging object is left unchanged. The acceleration a' of the punk and the radius r' of the circle are now given by

A puck is moving in a circle in a circle of radius r_(0) with a constant speed v_(0) on a level frictionless table. A string is attached to the punk, which holds it in the circle, the string passes through a frictionless hole and is attached on the other end to a hanging object of mass M. The puck is mow made to move with a speed v' = 3v_(0) , but still in circle. The mass of the hanging object is left unchanged. The acceleration a' of the punk and the radius r' of the circle are now given by

A uniform disc of radius a and mass m, is rotating freely with angular speed omega in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc of the disc and rotates with it. The new angular speed is

A 2kg block lying on smooth table which is connected by a body of mass 1 kg by a string which passes through a pulley. Take 1 kg mass hanging vertically. Find the acceleration of block & tension in string.