A hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and mass $M$. It is suspended by a string in a liquid of density $\rho$, where it stays vertical. The upper surface of cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is
$\rho g (V + \pi R^2)$
$Mg$
$Mg - V \rho g$
$\rho g (V + \pi R^2 h)$
A vessel containing water is moving with a constant speed towards right along a straight horizontal path. if the vessel is given a constant retardation towards the right along a straight line, which of the above diagram represents the surface of the liquid?
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
A silver ingot weighing $2.1 kg$ is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of silver is $10.5$ . The tension in the string in $kg-wt$ is
A cubical block of wood $10 \,cm$ on a side floats at the interface between oil and water with its lower surface horizontal and $4\, cm$ below the interface. The density of oil is $0.6gc{m^{ - 3}}$. The mass of block is ...... $gm$
A body floats in a liquid contained in a beaker. The whole system as shown falls freely under gravity. The upthrust on the body due to the liquid is