$A$ light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $m_1 = 0.36 \text{ kg}$ and $m_2 = 0.72 \text{ kg}$. Taking $g = 10 \text{ m/s}^2$,find the work done (in joules) by the string on the block of mass $0.36 \text{ kg}$ during the first second after the system is released from rest.

An engine pumps up $100 \ kg$ of water through a height of $10 \ m$ in $5 \ s$. Given that the efficiency of the engine is $60\%$. If $g = 10 \ m \ s^{-2}$,the power of the engine is .............. $kW$.

$A$ pendulum of length $2\,m$ is released from point $P$ as shown in the figure. When it reaches point $Q$,it loses $10\%$ of its total energy due to air resistance. The velocity at $Q$ is .... $m/s$.

If a lighter body (mass $M_1$ and velocity $V_1$) and a heavier body (mass $M_2$ and velocity $V_2$) have the same kinetic energy,then

$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

$A$ particle of mass $m$ moving horizontally with velocity $v_0$ strikes a smooth wedge of mass $M$,as shown in the figure. After the collision,the ball starts moving up the inclined face of the wedge and rises to a height $h$. Suppose the particle,when it reaches the horizontal surface again,has a velocity $v_1$ with respect to the ground,and the wedge has a velocity $v_2$. Choose the correct statement$(s)$.