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?

$A$ horizontal force $12 \, N$ pushes a block weighing $1/2 \, kg$ against a vertical wall. The coefficient of static friction between the wall and the block is $0.5$ and the coefficient of kinetic friction is $0.35$. Assuming that the block is not moving initially,which one of the following choices is correct? (Take $g = 10 \, m/s^2$)

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

$A$ block of mass $M = 10\,kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $\mu = 0.05.$ When hit by a bullet of mass $m = 50\,g$ moving with speed $v,$ which gets embedded in it,the block moves and comes to a stop after moving a distance of $2\,m$ on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height $H,$ then neglecting energy losses and taking $g = 10\,m/s^2,$ the value of $H$ is close to ................. $km$.

$A$ force of $(2.6 \hat{i} + 1.6 \hat{j}) \text{ N}$ acts on a body of mass $2 \text{ kg}$. If the velocity of the body at time $t = 0$ is $(3.6 \hat{i} - 4.8 \hat{j}) \text{ ms}^{-1}$, the time at which the body will just have a velocity along the $x$-axis only is: (in $\text{ s}$)

$A$ body of mass $2 \,kg$ is acted upon by two forces each of magnitude $1 \,N$, making an angle of $60^{\circ}$ with each other. The net acceleration of the body (in $m/s^2$) is