Given $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$. How much distance in $cm$ will $m_2$ cover in $0.4 \, s$?

Two fixed frictionless inclined planes making an angle $30^\circ$ and $60^\circ$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

$A$ wooden block of mass $2\; kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25\; kg$ is placed on top of the block,the floor yields steadily and the block and the cylinder together go down with an acceleration of $0.1\; m/s^2$. What is the action of the block on the floor $(a)$ before and $(b)$ after the floor yields? Take $g = 10\; m/s^2$. Identify the action-reaction pairs in the problem.

On the horizontal surface of a truck,a block of mass $1 \; kg$ is placed $(\mu = 0.6)$. If the truck is moving with an acceleration of $5 \; m/s^2$,then the frictional force on the block will be: (in $; N$)

$A$ car accelerates on a horizontal road due to the forces exerted by

$A$ balloon of total mass $M$ and a fixed size starts coming down with an acceleration $f$ $(f < g)$. The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $f$ (assuming negligible air resistance) is