A uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is
$\sqrt {2gl}$
$\sqrt {gl}$
$\sqrt {4gl}$
$\sqrt {3gl}$
A body is falling under gravity from rest. When it loses a gravitational potential energy by $U,$ its speed increases to $v.$ The mass of the body shall be
Power applied to a particle varies with time as $P = (4t^3 -5t + 2)\,watt$, where $t$ is in second. Find the change is its $K.E.$ between time $t = 2$ and $t = 4 \,sec.$ ............... $\mathrm{J}$
A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is .............. $\mathrm{m} / \mathrm{s}$
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
Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30\,kg$ and velocity $1\,m/s$ and skater $B$ has a mass $20\,kg$ and velocity $2\,m/s$ . They meet and cling together. Their final velocity of the couple is ............. $\mathrm{m}/ \mathrm{s}$