$A$ & $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on frictionless surface connected by one spring. Natural length of spring is $L$ and force constant $K$. Initially spring is in natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along line joining $A$ & $B$ collide with $A$. In ideal condition maximum compression of spring is :-

- A
$v \sqrt[]{\frac{m}{2K}}$

- B
$ m \sqrt[]{\frac{v}{2K}}$

- C
$\sqrt{\frac{mv}{K}}$

- D
$\frac{mv}{2K}$

Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2\, s$ will be ............ $\mathrm{m}/ \mathrm{s}$

A force acts on a $3\, gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t -4t^2 + t^3$, where $x$ is in $meters$ and $t$ is in $seconds$ . The work done during the first $4\, second$ is .............. $\mathrm{mJ}$

A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

In the non-relativistic regime, if the momentum, is increased by $100\%$, the percentage increase in kinetic energy is

The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?

$(I)$ $R$ and $S$ moved in the same direction after the collision.

$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.

$(III)$ The mass of $R$ was greater than mass of $S.$