$A$ body of mass $2 \,kg$ thrown vertically from the ground with a velocity of $8 \,ms^{-1}$ reaches a maximum height of $3 \,m$. The work done by the air resistance is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,J$)

$A$ 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 particle starts moving up the inclined face of the wedge and rises to a height $h$. The maximum height $h$ attained by the particle is:

$A$ body of mass $5 \,kg$ falls from a height of $30 \,m$. If all its mechanical energy is converted into heat,then the heat produced will be ........ $cal$.

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.

$A$ particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a particle of mass $10m$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1} = \sqrt{n} \sin \theta_{2}$,then the value of $n$ is:

$A$ point mass of $1 \, kg$ collides elastically with a stationary point mass of $5 \, kg$. After their collision, the $1 \, kg$ mass reverses its direction and moves with a speed of $2 \, m/s$. Which of the following statement(s) is (are) correct for the system of these two masses?
$(A)$ Total momentum of the system is $3 \, kg \cdot m/s$
$(B)$ Momentum of $5 \, kg$ mass after collision is $4 \, kg \cdot m/s$
$(C)$ Kinetic energy of the centre of mass is $0.75 \, J$
$(D)$ Total kinetic energy of the system is $4 \, J$