$A$ packet of weight $W$ dropped from a parachute strikes the ground and comes to rest with retardation equal to twice the acceleration due to gravity. The force exerted on the ground is

$A$ 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

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?

Block $A$ of mass $m$ and block $B$ of mass $M$ are connected by a massless spring over a pulley on a rough plane with coefficient of friction $\mu$. $A$ force $F$ is applied on block $A$ to the left. Find the minimum value of $M$ to move the block $A$ towards the right.

$A$ 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 ................. $km$.

Two wedges each of mass $600 \ g$ are placed next to each other on a rough horizontal surface. The coefficient of static friction between the wedges and the surface is $0.4$. $A$ cube of mass $M$ is balanced on the wedges as shown in the figure. If there is no friction between the cube and wedges,the largest mass $M$ of the cube that can be balanced without motion of the wedges is . . . . . . $kg$.