A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000\, kg$. The area of cross section a of piston carrying the load is $425\, cm ^{2}$. What is the maximum pressure () would smaller piston have to bear ?
$15.82 \times 10^{5} Pa$
$1.12 \times 10^{5} Pa$
$2.63 \times 10^{5} Pa$
$6.92 \times 10^{5} Pa$
Two non-mixing liquids of densities $\rho $ and $n \rho \,(n > 1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\rho L (\rho < 1)$ in the denser liquid. The density $d$ is equal to
A cylindrical vessel filled with water upto height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of vessel and plane is $\mu$ and total mass of water plus vessel is $M$. What should be minimum diameter of hole so that the vessel begins to move on the floor if plug is removed (here density of water is $\rho$ )
A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of $g/3,$ the fraction of volume immersed in the liquid will be
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
An empty glass jar is submerged in tank of water with open mouth of the jar downwards, so that air inside the jar is trapped and cannot get out. As the jar is pushed down slowly, the magnitude of net buoyant force on the system of volume of gas trapped in the jar and the jar