To maintain a speed of $80\,km/h$ by a bus of mass $500\,kg$ on a plane rough road for $4\,km$ distance,the work done by the engine of the bus will be $........\,kJ$. [The coefficient of friction between the tyre of the bus and the road is $0.04$].

$A$ bullet of mass $10\, g$ moving horizontally with a velocity of $400\, m s^{-1}$ strikes a wood block of mass $2\, kg$ which is suspended by a light inextensible string of length $5\, m$. As a result,the centre of gravity of the block is found to rise a vertical distance of $10\, cm$. The speed of the bullet after it emerges out horizontally from the block will be ................... $m s^{-1}$.

$A$ body of mass $4 \ kg$ is moving with a momentum of $8 \ kg \ m/s$. $A$ force of $0.2 \ N$ acts on it in the direction of motion for $10 \ s$. The increase in kinetic energy in joules is:

State if each of the following statements is true or false. Give reasons for your answer.
$(a)$ In an elastic collision of two bodies,the momentum and energy of each body is conserved.
$(b)$ Total energy of a system is always conserved,no matter what internal and external forces on the body are present.
$(c)$ Work done in the motion of a body over a closed loop is zero for every force in nature.
$(d)$ In an inelastic collision,the final kinetic energy is always less than the initial kinetic energy of the system.

$A$ bullet of mass $30 \,g$ moving with $700 \,ms^{-1}$ collides with a block of mass $4 \,kg$ hanging by a string of length $0.4 \,m$. After the collision, the block rises to a height of $0.2 \,m$. Find the velocity of the bullet when it emerges from the block. (in $\,ms^{-1}$)

$A$ ball of mass $1 \ kg$ moving with a velocity of $0.4 \ m/s$ collides with another ball of the same mass at rest. After the collision,the first ball moves with a velocity of $0.3 \ m/s$ in a direction perpendicular to the initial direction. Find the magnitude of the momentum $\vec{P}$ of the second ball in $kg \cdot m/s$.