A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are
$7.174 \times 10^6\, erg,\, 2.626 \times 10^6\, erg$
$8.2 \times 10^6\, erg,\, 2.2 \times 10^6 \,erg$
$2.6 \times 10^6 \,erg,\, 5.6 \times 10^6\, erg$
$3.6 \times 10^6\, erg,\, 6.2 \times 10^6\, erg$
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 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
Work done by the frictional force is
In the figure shown the potential energy $(U)$ of a particle is plotted against its position $'x'$ from origin. The particle at
The kinetic energy $K$ of a particle moving along a circle of radius $R$ depends upon the distance $s$ as $K = as^2$. The force acting on the particle is