A body having volume $V$ and density $\rho$ is attached to the bottom of a container as shown. Density of the liquid is $d( > \rho )$. Container has a constant upward acceleration $a.$ Tension in the string 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

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 block of ice floats in an oil in a vessel when the ice melts, the level of oil will ..............

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

Acontainer of large surface area is filled with liquid of density $\rho$ .Acubical block of side edge $a$ and mass $M$ is floating in it with four-fifth of its volume submerged. If a coin of mass $m$ is placed gently on the top surface of the block is just submerged. $M$ is