A spring of spring constant $5 \times 10^3\, N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\, cm$ is .............. $\mathrm{N}$ $-$ $\mathrm{m}$
$6.25$
$12.50$
$18.75$
$25$
The mass of the bob of a simple pendulum of length $L$ is $m$. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively
Two identical particles are moving with same velocity $v$ as shown in figure. If the collision is completely inelastic then
A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is
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 .............
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