$A$ 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?

$(a)$ 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. $(g = 10 \, m s^{-2})$

What happens to the kinetic energy when
$(i)$ the mass of the body is doubled at constant velocity?
$(ii)$ the velocity of the body is doubled at constant mass?
$(iii)$ the mass of the body is doubled but the velocity is reduced to half?

$A$ body is moving with constant speed over a frictionless surface. What is the work done by the weight of the body?

$(a)$ Give two conditions for work to be done.
$(b)$ What is the work done by frictional force on an object when dragged along a rough surface?
$(c)$ Relate power and work.
$(d)$ $A$ machine does $1960 \, J$ of work in $4 \, \text{minutes}$. What is the power?

$(a)$ Define work. State two factors on which the magnitude of work depends.
$(b)$ $A$ car and a truck have the same speed of $30 \, m/s$. If their masses are in the ratio $1:3$,find the ratio of their kinetic energy.