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 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
A force of $\left( {2\hat i + 3\hat j + 4\hat k} \right)\,N$ acts on a body for $4\, sec$ and produces a displacement of $\left( {3\hat i + 4\hat j + 5\hat k} \right)\,m.$ The power used is ............. $\mathrm{W}$
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
Two blocks $A$ and $B$ of masses $1\,\,kg$ and $2\,\,kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.s$ of both the blocks is
A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be