The mass of a lift is $500\, kg$. When it ascends with an acceleration of $2\, m/s^2$,the tension in the cable will be........... $N$ $[g = 10\, m/s^2]$

$A$ 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:

Two masses of $4\, kg$ and $5 \,kg$ are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of the $5\, kg$ mass is ........... $m/s^2$.

Two blocks are in contact on a frictionless table. One has mass $m$ and the other $2\,m$. $A$ force $F$ is applied on $2\,m$ as shown in the figure. Now,the same force $F$ is applied from the right on $m$. In the two cases respectively,what is the ratio of the contact force between the two blocks?

$A$ smooth right-angled wedge of mass $M$ is kept on a smooth horizontal surface as shown. $A$ mass $m$ is released from the top of the wedge. When $m$ reaches the ground, its speed is $V$. Find the work done by the normal contact force on $m$ while it comes down to the ground.

$A$ 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