A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is

Two bodies of masses $m_1$ and $m_2$ are moving with same kinetic energy. If $P_1$ and $P_2$ are their respective momentum, the ratio $\frac{P_1}{P_2}$ is equal to

If $F = 2x^2 -3x -2$, then choose correct option

After head on elastic collision between two balls  of equal masses , one is observed to have a speed of  $3\,\,m/s$  along positive  $x-$ axis and the other has a speed of  $2\,\,m/s$  along negative $x$  axis. The original velocities of the balls are

Underline the correct alternative :

$(a)$ When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.

$(b)$ Work done by a body against friction always results in a loss of its kinetic/potential energy.

$(c)$ The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.

$(d)$ In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.