A shell is fired from a canon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces come to rest. The speed of the other piece immediately after the explosion is

- A
$3V\, cos\theta$

- B
$2V\, cos\theta$

- C
$\frac{3}{2}\,V\cos \theta $

- D
$V\, cos\theta$

If the kinetic energy of a body is directly proportional to time $t$, the magnitude of force acting on the body is

$(i)$ directly proportional to $\sqrt t$

$(ii)$ inversely proportional to $\sqrt t$

$(iii)$ directly proportional to the speed of the body

$(iv)$ inversely proportional to the speed of body

A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$

A particle of mass $M$ starting from rest undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, then power delivered to the particle in time $T$ is

A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball's vertical velocity $v$ with time between the time ${t_1}$ as it hits the bat and time $t_2$ when it touches the ground

A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is