Two bodies of masses $10\; kg$ and $20\; kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. $A$ horizontal force $F = 600\; N$ is applied to $(i)\; A$,$(ii)\; B$ along the direction of the string. What is the tension in the string in each case?

$A$ uniform thick string of length $8\, m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $8\, N$ from one end. The tension in the string at $3\, m$ from the force applied is ........ $N$.

$A$ small block of mass $m$ is placed on a wedge of mass $M$ as shown,which is initially at rest. All the surfaces are frictionless. The spring attached to the other end of the wedge has a force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down,then the maximum retardation of $M$ is:

$A$ force $F = 10t$ acts on a block of mass $m = 10 \, kg$ as shown in the figure. The coefficient of friction is $\mu = 0.4$. Find the time $t$ when the block loses contact with the surface.

Ten one-rupee coins are placed on top of each other on a table. Each coin has mass $m$. The reaction force of the $6^{th}$ coin (counted from the bottom) on the $7^{th}$ coin is .......... $mg$.

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is