A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is
$MgL$
$\frac{{MgL}}{3}$
$\frac{{MgL}}{9}$
$\frac{{MgL}}{18}$
A particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then
A bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is
The force acting on a body moving along $x-$ axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at
A 3.628 kg freight car moving along a horizontal rail road spur track at $7.2\; km/hour$ strikes a bumper whose coil springs experiences a maximum compression of $30 \;cm$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15\; cm$ is [2013]
(a) $12.1 \times 10^4\;J$ (b) $121 \times 10^4\;J$ (c) $1.21 \times 10^4\;J$ (d) $1.21 \times 10^4\;J$
$2$ particles of mass $1\,Kg$ and $5\,kg$ have same momentum, calculate ratio of their $K.E.$