A particle of mass $m$ strikes the ground inelastically, with coefficient of restitution $e$
$\frac{{\tan \,\alpha }}{{\tan \,\theta }} = e$
$\frac{{\tan \,\theta }}{{\tan \,\alpha }} = e$
${\tan ^2}\,\theta + {\tan ^2}\,\alpha = 1$
${\tan ^2}\,\theta + {\tan ^2}\,\alpha = {e^2}$
If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)
The work done by a force $\vec F\, = \,( - \,6{x^3}\,\hat i)N$ , in displacing a particle from $x = 4\,m$ to $x = -\,2\,m$ is .............. $\mathrm{J}$
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 car is moving on a straight horizontal road with a speed $v.$ If the coefficient of friction between the tyres and the road is $\mu ,$ the shortest distance in which the car can be stopped is
A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time