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 given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid
The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $‘A’$ and top area $‘a’$ and the walls of the vessel are inclined at an angle $30^o$ with the vertical.A liquid of density $\rho$ fills both the sections upto a height $2h$. Neglecting atmospheric pressure.
A solid sphere of density $\eta$ $( > 1)$ times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
A hollow sphere has inner volume half the outer volume. Its $4/5\,th$ part is submerged when placed in water. The density of material is
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?