A wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed the cube is $2\,cm$ above water level. The side of cube is ........ $cm$
$5$
$10$
$15$
$20$
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
A man is sitting in a boat which is floating in a pond. If the man drinks same water from the pond, the level of water in pond will
A body floats in a liquid contained in a beaker. If the whole system as shown in figure falls freely under gravity, then the upthrust on the body due to liquid is
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 $\rho$ )
Mumbai needs $1.4 \times 10^{12} L$ of water annually. Its effective surface area is $600 \,km ^2$ and it receives an average rainfall of $2.4 \,m$ annually. If $10 \%$ of this rain water is conserved, it will meet approximately