$A$ girl of mass $35 \, kg$ sits on a trolley of mass $5 \, kg$. The trolley is given an initial velocity of $4 \, m \, s^{-1}$ by applying a force. The trolley comes to rest after covering a distance of $16 \, m$. $(a)$ What is the work done on the trolley? $(b)$ What is the work done by the girl?

$(a)$ Two bodies have equal masses and are moving with uniform velocities of $2\,v$ and $3\,v$. What is the ratio of their kinetic energies?
$(b)$ $A$ mass is dropped from height $h$. At halfway to the ground,what is the total energy?

$A$ mass of $10 \, kg$ is dropped from a height of $50 \, cm$. Find its:
$(a)$ Potential energy just before dropping.
$(b)$ Kinetic energy just on touching the ground.
$(c)$ Velocity with which it hits the ground. (Given: $g = 10 \, m s^{-2}$)

$(a)$ The Earth,moving around the Sun in a circular orbit,is acted upon by a force,and hence work must be done on the Earth by the force. State whether the statement is correct or not. Give reasons for your answer.
$(b)$ $A$ coolie holding a heavy box is waiting at the bus stand for $15$ minutes. How much work is done by him?
$(c)$ $A$ man weighing $70 \, kg$ carries a weight of $10 \, kg$ to the top of a tower $100 \, m$ high. Calculate the work done by the man. $(g = 10 \, m s^{-2})$

$(a)$ An arrow moves forward when released from a stretched bow. Explain the transformation of energy in the process.
$(b)$ $A$ boy of mass $50 \, kg$ climbs up a vertical height of $100 \, m$. Calculate the amount of potential energy he gains.

An automobile engine propels a $1000 \,kg$ car $(A)$ along a levelled road at a speed of $36 \,km \,h^{-1}$. Find the power if the opposing frictional force is $100 \,N$. Now,suppose after travelling a distance of $200 \,m$,this car collides with another stationary car $(B)$ of the same mass and comes to rest. Let its engine also stop at the same time. Now car $(B)$ starts moving on the same level road without its engine started. Find the speed of the car $(B)$ just after the collision.