$A$ $100 \ kg$ 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. The recoil velocity of the gun is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $ms^{-1}$)

$A$ block $B$ is placed on block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks,whereas the ground on which the block $A$ is placed is taken to be smooth. $A$ horizontal force $F$,increasing linearly with time,begins to act on $B$. The acceleration $a_A$ and $a_B$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is

Two blocks,$4\, kg$ and $2\, kg$,are sliding down an inclined plane as shown in the figure. The acceleration of the $2\, kg$ block is ........ $m/s^2$.

$A$ balloon of mass $M$ is descending at a constant acceleration $\alpha$. When a mass $m$ is released from the balloon,it starts rising with the same acceleration $\alpha$. Assuming that its volume does not change,what is the value of $m$?

Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. Find the velocity of $m_2$ at $t = 0.4 \, s$ in $cm/s$.

Two cars of masses $m_1$ and $m_2$,joined back to back by a massless compressed spring,are at rest on a horizontal rough road. When the compression of the spring is suddenly removed,the cars move away from each other and come to rest due to friction. If the frictional force is the same on both cars,what is the ratio of their stopping times?