A bullet of mass 10 g and speed `500 m//s` is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.

A bullet of mass 20 g is fired with speed 400 m s^-1 by a gun of mass 8 kg. Find the recoil velocity of the gun.

A bullet of mass 20 g moving with a speed of 500ms^(-1 ) strikes a wooden block of mass 1 kg and gets embedded in it. Find the speed with which block moves along with the bullet.

A bullet of mass 25 g moving with a speed of 100 m/s pierces a bag full of sand kept adjacent to a wall. The bullet stops in the bag after 0.05 second. Find The force exerted by the sandbag on the bullet.

A bullet of mass 25 g moving with a speed of 100 m/s pierces a bag full of sand kept adjacent to a wall. The bullet stops in the bag after 0.05 second. Find The acceleration of the bullet (assuming uniform).

A bullet of mass 40 g hits a mud wall with speed 400 m s^-1 . The bullet stops after penetrating 50 cm inside the wall. Find the average resistive force exerted by the wall on the bullets.

A particle of mass 150 g is attached to one end of a massless inextensible string It is made to describe a vertical circle of radius 1 m When the string is making an angle of 48.2^(@) with the vertical , its instantaneous speed is 2 m//s What is the tension in the string in this position ? Would this particle be able to complte its circular path?(Take g=10 m s^(-2) ).

A small stone of mass 200 g is tied to one end of a string of length 80 cm . Holding the other end in hand , the stone is whirled into a vertical circle What is the minimum speed that needs to be imparted at the lowest point of the circular path , so that the stone is just able to complete the vertical circle ? what would be the tension at the lowest point of circular path ? (Take g = 10 m//s^(2) ) .

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1 . The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

A massless string of length 1.2 m, has a breaking strength of 2 kg wt. A stone of mass 0.4 kg, tied to one end of the string, is made to move in a vertical circle, by holding the other end in the hand. Can the particle describe the vertical circle? (Take g = 10 m s^-2 )