$A$ disc of mass $0.2 \ kg$ is kept floating in air without falling by vertically firing bullets each of mass $0.05 \ kg$ on the disc at the rate of $10$ bullets per second. If the bullets rebound with the same speed,then the speed of each bullet is (Acceleration due to gravity $g = 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

In a tug-of-war contest,two men pull on a horizontal rope from opposite sides. The winner will be the man who

$A$ force acts for $20\,s$ on a body of mass $20\,kg$,starting from rest,after which the force ceases and the body travels $50\,m$ in the next $10\,s$. The value of the force is $..........\,N$.

$A$ cone of radius $r$ and height $h$ rests on a rough horizontal surface. The coefficient of friction between the cone and the surface is $\mu$. $A$ gradually increasing horizontal force $F$ is applied to the vertex of the cone. The largest value of $\mu$ for which the cone will slide before it topples is

The masses of blocks $A$ and $B$ are $100 \, kg$ and $200 \, kg$ respectively. The coefficient of friction between $A$ and $B$ is $0.2$,and the coefficient of friction between $B$ and the ground is $0.3$. What force $F$ (in $N$) must be applied to block $B$ to make it move?

Shown in the diagram is a system of two bodies,a block of mass $m$ and a disc of mass $4m$,held in equilibrium. If the string $3$ is burnt,find the acceleration of the disc. Neglect the masses of the pulleys $P$ and $Q$. The coefficient of friction between the block and the horizontal surface is $0.5$ and the friction between the disc and the string is zero. (Take $g = 10 \ m/s^2$)