A solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of cavity radius to that of outer radius of sphere is
$\frac{{{{\left( {28} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {30} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {26} \right)}^{1/3}}}}{3}$
$\frac{{{{\left( {24} \right)}^{1/3}}}}{3}$
A thin vertical uniform wooden rod is pivoted at the top and immersed in water as shown. The container is slowly raised. At a certain moment, the equilibrium becomes unstable. If density of water is $9/5$ times the density of wood, then ratio of total length of rod to the submerged length of rod, at that moment is
A cork is submerged in water by a spring attached to the bottom of a pail. When the pail is kept in a elevator moving with an acceleration downwards, the spring length
A sample of metal weighs $210 gm$ in air, $180 gm$ in water and $120 gm$ in liquid. Then relative density $(RD) $ of
A small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500\ kg/m^3$ and that of liquid is $1000\ kg/m^3$ If the ball comes momeritariiy at rest at $t = 2\ sec$ then initial height of the ball from surface of liquid was ..... $m$ (neglect viscosity)
A drinking straw is dipped in a pan of water to depth d from the surface (see figure below). Now water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result, its height $y$ from the surface of the water varies periodically. Ignoring damping, the equation for $y$ is ( $g$ is the acceleration due to gravity):