A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$

A bullet of mass $m$ and speed $v$ hits a pendulum bob of mass $M$ at time $t_1$, and passes completelythrough the bob. The bullet emerges at time $t_2$ with a speed of $v/2$. The pendulum bob is suspended by a stiff rod of length $l$ and negligible mass. After the collision, the bob can barely swing through a complete vertical circle.At time $t_3$, the bob reaches the highest position.What quantities are conserved in this process?

Write the law of conservation of total linear momentum for the system of particle.

A neutron moving with a speed $'v'$ makes a head on collision with a stationary hydrogen atom in ground state . The minimum kinetic energy of the neutron for which inelastic collision will take place is....$eV$

$A$ projectile of mass $"m"$ is projected from ground with a speed of $50 \,m/s$ at an angle of $53^o$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle coming to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground are:

A body falls towards earth in air. Will its total mechanical energy be conserved during the fall ? Justify.