Masses of $10\, kg$ and $20\, kg$ are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant shown,the $10\, kg$ mass has an acceleration of $12\, m/s^2$. What is the acceleration of the $20\, kg$ mass in $m/s^2$?

Two identical balls are connected by a massless and inextensible thread of length $L$. The system is in gravity-free space with the thread just taut. At $t = 0$,each ball is imparted a velocity $v$; one ball is given a velocity towards the other ball,and the other is given a velocity perpendicular to the first. Then,

$A$ ball connected with a string is released at an angle of $45^{\circ}$ with the vertical,as shown in the figure. If the mass of the box is equal to the mass of the ball,the acceleration of the box at this instant will be:

$Assertion$: Two bodies of masses $M$ and $m$ $(M > m)$ are allowed to fall from the same height. If the air resistance for each is the same,then both bodies will reach the Earth simultaneously.
$Reason$: For the same air resistance,the acceleration of both bodies will be the same.

$A$ box '$A$' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time '$t$',it decelerates. Then the reaction $R$ by the floor on the box is given best by

$A$ block of mass $5\,kg$ starting from rest is pulled up on a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal with an effective acceleration of $1\,m/s^2$. The power delivered by the pulling force at $t = 10\,s$ from the start is $.....\,W$. [Use $g = 10\,m/s^2$] (calculate the nearest integer value).