$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

The arrangement of a two-block system is as shown. Assuming the surfaces to be frictionless,the net force acting on the $1 \, kg$ and $2 \, kg$ blocks are,respectively:

The figure shows a boy on a horizontal platform $A$ on a smooth horizontal surface,holding a rope attached to a box $B$. The boy pulls the rope with a constant force of $50 \ N$. (The boy does not slip over the platform). The combined mass of platform $A$ and the boy is $250 \ kg$,and that of box $B$ is $500 \ kg$. The velocity of $A$ relative to the box $B$,$5 \ s$ after the boy on $A$ begins to pull the rope,will be ............ $m/s$.

$A$ mass of $1 \ kg$ is suspended by means of a thread. The system is
$(i)$ lifted up with an acceleration of $4.9 \ ms^{-2}$
(ii) lowered with an acceleration of $4.9 \ ms^{-2}$.
The ratio of tension in the first and second case is

The figure shows a uniform rod of length $30 \,cm$ having a mass of $3.0 \,kg$. The rod is pulled by constant forces of $20 \,N$ and $32 \,N$ as shown. Find the force exerted by the $20 \,cm$ part of the rod on the $10 \,cm$ part (all surfaces are smooth).

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?