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
$\sqrt {2gl}$
$\sqrt {gl}$
$\sqrt {4gl}$
$\sqrt {3gl}$
The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
After on head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are
Figure shows the vertical section of frictionless surface. A block of mass $2\, kg$ is released from the position $A$ ; its $KE$ as it reaches the position $C$ is ............ $\mathrm{J}$
A rope is used to lower vertically a block of mass $M$ by a distance $x$ with a constant downward acceleration $\frac{g}{2}$. The work done by the rope on the block is
If $F = 2x^2 -3x -2$, then choose correct option