A uniformly charged solid sphere of radius $$R$$ has potential $${V_0}$$ (measured with respect to $$\infty $$) on its surface. For this sphere the equipotential surfaces with potentials $${{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}} \over 4}$$ and $${{{V_0}} \over 4}$$ have radius $${R_1},\,\,{R_2},\,\,{R_3}$$ and $${R_4}$$ respectively. Then

In the given circuit, charges $${Q_2}$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\,\mu F$$ to $$3\mu F.$$ $${Q_2}$$ as a function of $$'C'$$ is given properly by:
$$\left( {figures\,\,are\,\,drawn\,\,schematically\,\,and\,\,are\,\,not\,\,to\,\,scale} \right)$$

For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its displacement $$d.$$ Which one of the following represents these correctly?
$$(graphs$$ $$are$$ $$schematic$$ $$and$$ $$not$$ $$drawn$$ $$to$$ $$scale)$$

A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is added to its bob, the time period changes to $${T_{M.}}$$ If the Young's modulus of the material of the wire is $$Y$$ then $${1 \over Y}$$ is equal to :
($$g=$$ $$gravitational$$ $$acceleration$$)