In the figure,two blocks are connected by a uniform strut attached to each block with frictionless pins. Block $A$ weighs $400 \, N$,block $B$ weighs $300 \, N$,and the strut $AB$ weighs $200 \, N$. If $\mu = 0.25$ under block $B$,determine the minimum coefficient of friction under block $A$ to prevent motion.

$A$ 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 the figure,a ball of mass $m$ is tied with two strings of equal length as shown. If the rod is rotated with angular velocity $\omega$,then

$A$ man pulls a block heavier than himself with a light horizontal rope. The coefficient of friction is the same between the man and the ground,and between the block and the ground.

Consider a system of blocks $A$, $B$, and $X$ as shown in the figure. The blocks $A$ and $B$ have equal mass $m$ and are connected by a massless string through a massless pulley. The coefficient of friction between block $A$ and $X$, and between block $B$ and $X$, is $\mu = 0.5$. If block $X$ moves on the horizontal frictionless surface, what should be its minimum acceleration $a$ such that blocks $A$ and $B$ remain stationary relative to $X$? ($g =$ acceleration due to gravity.)

An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]