$A$ constant force $F = m_2g/2$ is applied on the block of mass $m_1$ as shown in the figure. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

$A$ $100 \, kg$ gun fires a ball of $1 \, kg$ horizontally from a cliff of height $500 \, m$. It falls on the ground at a distance of $400 \, m$ from the bottom of the cliff. Find the recoil velocity of the gun. (Acceleration due to gravity $g = 10 \, m/s^2$) (in $, m/s$)

Three blocks with masses $m$,$2m$,and $3m$ are connected by strings,as shown in the figure. After an upward force $F$ is applied on block $m$,the masses move upward at a constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

$A$ block $A$ with mass $100\, kg$ is resting on another block $B$ of mass $200\, kg$. As shown in the figure,a horizontal rope tied to a wall holds block $A$. The coefficient of friction between $A$ and $B$ is $0.2$,while the coefficient of friction between $B$ and the ground is $0.3$. The minimum required force $F$ to start moving block $B$ will be ........ $N$.

In the figure shown,all surfaces are frictionless,and the mass of the block is $m = 1\, kg$. The block and wedge are held initially at rest. Now,the wedge is given a horizontal acceleration of $a = 10\, m/s^2$ by applying a force on the wedge,such that the block does not slip on the wedge. Calculate the work done by the normal force in the ground frame on the block in $\sqrt{3}$ seconds. (Assume $\tan \theta = a/g = 1$,so $\theta = 45^\circ$)

What is the relationship between $W_1$ and $W_2$?