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 ........ $m / s ^2$

$A$ particle of mass m is constrained to move on $x$ -axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example, when the particle is to the left of $E, F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards left from the equilibrium position $E$ and released from rest at $t = 0.$ Velocity - time graph of the particle is

Define impulse of force. Time derivative of momentum gives which physical quantity ?

An $80\, kg$ person is parachuting and is experiencing a downward acceleration of $2.8\, m/s^2$. The mass of the parachute is $5\, kg$. The upward force on the open parachute is  ........... $N$ (Take $g = 9.8\, m/s^2$)

A uniform sphere of weight $W$ and radius $5\, cm$ is being held by a string as shown in the figure. The tension in the string will be

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