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 :
($$g=$$ $$gravitational$$ $$acceleration$$)

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

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?
$$(graphs$$ $$are$$ $$schematic$$ $$and$$ $$not$$ $$drawn$$ $$to$$ $$scale)$$

From a solid sphere of mass $$M$$ and radius $$R,$$ a spherical portion of radius $$R/2$$ is removed, as shown in the figure. Taking gravitational potential $$V=0$$ at $$r = \infty ,$$ the potential at the center of the cavity thus formed is:
($$G=gravitational $$ $$constant$$)