A stone tied to a string $L$ is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is as its lowest position and has a speed $u$. the magnitude of the change in its velocity as it reaches a position where the string is horizontal is
$\sqrt {{u^2} - 2gL} $
$\sqrt {2gL} $
$\sqrt {{u^2} - gL} $
$\sqrt {2\left( {{u^2} - gL} \right)} $
A force $F = - K(yi + xj)$ (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point $(a, 0)$ and then parallel to the y-axis to the point $(a, a)$. The total work done by the force F on the particles is
A small block of mass $m$ slides along a smooth frictional track as shown in the figure. If it starts from rest at $P$ , velocity of block at point $Q$ is
A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$, the height to which the disc will rise will be
A block of mass $0.50\, kg$ is moving with a speed of $2.00\, ms^{-1}$ on a smooth surface. It strikes another mass of $1.00\, kg$ and then they move together as a single body. The energy loss during the collision is .............. $\mathrm{J}$
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to