A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_0$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
more than half filled if $\rho_c$ is less than $0.5$
more than half filled if $\rho_c$ is less than $1.0$
half filled if $\rho_c$ is less than $0.5$
less than half filled if $\rho_c$ is less than $0.5$
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
A body of density $\rho'$ is dropped from rest at a height $h$ into a lake of density $\rho$ , where $\rho > \rho '$ . Neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface.
A vessel contain a liquid has a constant acceleration $19.6 \,m / s ^2$ in horizontal direction. The free surface of water get sloped with horizontal at angle ..........
A air bubble of radius $1\,cm$ in water has an upward acceleration $9.8\, cm\, s ^{-2}$. The density of water is $1\, gm\, cm ^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is$.......gm$
$\left( g =980 \,cm / s ^{2}\right)$
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