Level 1

Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times where as its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

A shell of mass, $20 \mathrm{g}$ is fired by a gun of mass $100 \mathrm{kg}.$ If the muzzle speed of the shell is $6 \mathrm{km} {\min }^{-1}$, what is the recoil speed of the gun?

The unit of momentum is

A bullet of $4 \mathrm{g}$ mass is fired from a gun of mass $4 \mathrm{kg}.$ If the bullet moves with the muzzle speed of $50{ \mathrm{ms}}^1,$ the impulse imparted to the gun and velocity of recoil of gun are 

A particle of mass $m$ initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T.$ It attains a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle, find $u.$

A particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be :

The resultant of two forces acting at an angle of $150°$ is $10 \mathrm{kg}$ wt and is perpendicular to one of the forces. The other force is :

Two blocks of masses $M_1$ and $M_2$ are connected to each other through a light spring as shown in figure. If we push mass $M_1$ with force $F$ and cause acceleration $a_1$ in mass $M_1$, what will be the magnitude of acceleration in $M_2$?