$A$ balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed so that the balloon moves up with double the acceleration $2a_0$ is:

An elevator of mass $500 \,kg$ is ascending upwards with a constant acceleration $a=2 \,m/s^2$. What is the work done by the tension in the elevator cable during its climb by $12 \,m$ (in $\,kJ$)? (Take $g=10 \,m/s^2$)

$A$ block of mass $M$ is lying on a horizontal frictionless surface. One end of a uniform rope of mass $M/2$ is fixed to the block, which is pulled in the horizontal direction by applying a force $F$ at the other end. The tension in the middle of the rope will be

$A$ block of mass $18.5 \ kg$ kept on a smooth horizontal surface is pulled by a rope of $3 \ m$ length by a horizontal force of $40 \ N$ applied to the other end of the rope. If the linear density of the rope is $0.5 \ kg \ m^{-1}$ and initially the block is at rest,the time in which the block moves a distance of $9 \ m$ is: (in $s$)

Two blocks of $7\,kg$ and $5\,kg$ are connected by a heavy rope of mass $4\,kg$. An upward force of $200\,N$ is applied as shown in the diagram. The tension at the top of the heavy rope at point $P$ is ....... $N$ $(g = 10\,m/s^2)$.

Three blocks of masses $3\, kg, 2\, kg$,and $1\, kg$ are placed side by side on a smooth surface as shown in the figure. $A$ horizontal force of $12\, N$ is applied to the $3\, kg$ block. The net force on the $2\, kg$ block is ............ $N$.