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 $m/s^2$?

$A$ pebble of mass $0.05 \, kg$ is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,$(a)$ during its upward motion,$(b)$ during its downward motion,$(c)$ at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance.

What force should be applied on the wedge so that the block over it does not move? (All surfaces are smooth)

At time $t=0$,a force $F=\alpha t$,where $t$ is time in seconds,is applied to a body of mass $1 \text{ kg}$,resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal,then the velocity of the body at the moment of its breaking off the plane is

$A$ string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by

Given in the figure are two blocks $A$ and $B$ of weight $20\ N$ and $100\ N,$ respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$,the frictional force applied by the wall on block $B$ is ........... $N$.