A cone of radius $R$ and height $H$, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is
$\rho \pi gHR^2$
$\pi \rho HR^2$
$\frac{4}{3}$ $ \pi \rho gHR^2$
$\frac{2}{3}$ $ \pi \rho gHR^2 $
There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the container
A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$ as shown. Then the angle of inclination $ \theta $ of free surface is :
A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water
Write and prove Archimedes principle.
An object suspended by a wire stretches it by $10 \,mm$. When object is immersed in a liquid the elongation in wire reduces by $\frac{10}{3} \,mm$. The ratio of relative densities of the object and liquid is ............