Work done in time $t $ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time ${t_1}$ as a function of time $t$ is given by
$\frac{1}{2}m\frac{v}{{{t_1}}}{t^2}$
$m\frac{v}{{{t_1}}}{t^2}$
$\frac{1}{2}{\left( {\frac{{m\,v}}{{{t_1}}}} \right)^2}{t^2}$
$\frac{1}{2}m\frac{{{v^2}}}{{t_1^2}}{t^2}$
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c = k^2rt^2$, The power delivered to the particle by the forces acting on it is
The bob of a pendulum of length $l$ is pulled aside from its equilibrium position through an angle $\theta $ and then released. The bob will then pass through its equilibrium position with speed $v$ , where $v$ equals
A neutron travelling with a velocity $v$ and $K.E.$ $E $ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is
$2$ particles of mass $1\,Kg$ and $5\,kg$ have same momentum, calculate ratio of their $K.E.$
A rifle bullets loses $\left(\frac{1}{20}\right)^{th}$ of its velocity in passing through a plank. Assuming that the plank exerts a constant retarding force, the least number of such planks required just to stop the bullet is .............