Two masses of $10 \,kg$ and $20 \,kg$ respectivety are connected by a massless spring as shown in fig. A force of $200 \,N$ acts on the $20 \,kg$ mass At the instant shown the $10 \,kg$ mass has acceleration $12 \,m / s ^2$ towards right. The acceleration of $20 \,kg$ mass at this instant is ........ $m / s ^2$

Consider a frame that is made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{ P }$ of magnitude $100 \;N$ is applied at point $A$ of the frame. Suppose the force is $\overrightarrow{ P }$ resolved parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $xN$. The value of $x$, to the nearest integer, is ............

[Given : $\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819$ $\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]$

In the system shown in the adjoining figure, the tension $T_2$ is

A parachutist with total weight $75 \,kg$ drops vertically onto a sandy ground with a speed of $2 \,ms ^{-1}$ and comes to halt over a distance of $0.25 \,m$. The average force from the ground on her is close to ............ $N$

In a hydrogen atom, the distance between the electron and proton is $2.5 \times {10^{ - 11}}\,m$. The electrical force of attraction between them will be

Give the magnitude and direction of the net force acting on a stone of mass $0.1\; kg$,

$(a)$ just after it is dropped from the window of a stationary train,

$(b)$ just after it is dropped from the window of a train running at a constant velocity of $36 \;km/h$,

$(c)$ just after it is dropped from the window of a train accelerating with $1\; m s^{-2}$,

$(d)$ lying on the floor of a train which is accelerating with $1\; m s^{-2}$, the stone being at rest relative to the train.

Neglect air resistance throughout.