A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{{2{r^2}}}$ Its total energy is
$\;\frac{k}{{2{a^2}}}$
Zero
$ - \frac{3}{2}\;\frac{k}{{{a^2}}}$
$ - \frac{k}{{4{a^2}}}$
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^2$, find the work done (in joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.
A ball of mass $m$ moves with speed $v$ and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is
A ball is released from a height of $10\, m$. If after the impact there is loss of $40\%$ in its energy, the ball shall rise upto- ................. $\mathrm{m}$
A block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of spring constant ?
$A$ small bucket of mass $M\, kg$ is attached to $a$ long inextensible cord of length $L\, m$ . The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up $m\, kg$ of water and swings up to a height $h$. The height $h$ in meters is