$A$ lift of mass $2000 \ kg$ starts from rest in the basement and moves to the fourth floor,which is at a height of $25 \ m$. As it passes the fourth floor,its speed is $3 \ ms^{-1}$. There is a constant frictional force of $500 \ N$ acting on it. Calculate the work done by the lift's motor in $kJ$.

$A$ wooden block of mass $M$ is suspended by a string. $A$ bullet of mass $m$ passes through the block with velocity $v$ and emerges with a velocity $v/2$ in the same direction. To what height will the block rise?

$A$ ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \text{ m/s}$ and the coefficient of restitution is $0.75$. The total distance travelled by the ball before it comes to rest is (acceleration due to gravity $= 10 \text{ m/s}^2$) (in $\text{ m}$)

$A$ small block of mass $200 \ g$ is placed on a horizontal slab at a height of $2 \ m$ above the floor. The block is pressed against a horizontal spring fixed at one end to compress the spring by $10.0 \ cm$. Upon releasing, the block moves horizontally until it leaves the spring. Calculate the horizontal distance covered by the block after leaving the slab and just before hitting the ground. The spring constant is $50 \ N \ m^{-1}$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)

$A$ small bucket of mass $M \, kg$ is attached to a non-extensible string of length $L \, m$. The bucket is released from rest when the string is in a horizontal position. At its lowest point,the bucket scoops up $m \, kg$ of water and rises to a height $h$. The height $h$ (in meters) is:

On complete combustion,a litre of petrol releases heat equivalent to $3 \times 10^7 \, J$. In a test drive,a car weighing $1200 \, kg$ (including the driver) travels $15 \, km$ per litre while moving at a uniform speed on a straight track. Assuming that the friction offered by the road surface and air is uniform,calculate the force of friction acting on the car during the test drive,given that the efficiency of the car engine is $0.5$. (in $, N$)