A bolt of mass `0.3 kg` falls from the ceiling of an elevator moving down with an uniform speed of `7 ms^(-1)`. It hits the floor of the elevator (length of the elevator = 3m) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 ms^(-1) relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

A man of mass 50 kg is standing in an elevator. If elevator is moving up with an acceleration (g)/(3) then work done by normal reaction of elevator floor on man when elevator moves by a distance 12 m is (g=10 m//s^(2)) :-

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^(-1) to 3.5 m s^(-1) in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?

A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of 10 m s 1, (b) downwards with a uniform acceleration of 5 ms^(2) , (c) upwards with a uniform acceleration of 5 ms^(2) . What would be the readings on the scale in each case ? (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?

An observer 1.7m tall, is 20 sqrt3m away from a tower. The angle of elevation of the top of the tower from the eyes of the observer is 30^(@) . Find the height of the tower.

A steel wire of length 5 m and diameter 10^(-3) m is hanged vertically from a ceiling of 5.22 m height. A sphere of radius 0.1 m and mass 8tt kg is tied to the free end of the wire. When this sphere is oscillated like a simple pendulum, it touches the floor of the room in its velocity of the sphere in its lower most position. Calculate the velocity of the sphere in its lower Young's modulus for in its lower most position. Young's modulus for steel =1.994 xx 10 ^(11) Nm ^(-2).

On complete combustion a litre of petrol gives off heat equivalent to 3 xx 10^(7) J. In a test drive, a car weighing 1200 kg including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform. calculate the force of friction acting on the car during the test drive. if the efficiency of the car engine were 0.5.

From a point P on the ground the angle of elevation of the top of a 10m tail building is 30^(@) . A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45^(@) . Find the length of the flagstaff and the distance of the building from the point P. (You may take sqrt3= 1.732 )

A bullet of mass 0.012kg and horizontal speed 70 ms^(-1) strikes a block of wood of mass 0.4kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.