An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its sides,it was found that one-third of the volume of water spilled out. The acceleration was:

$A$ bucket contains water filled up to a height $h = 15 \ cm$. The bucket is tied to a rope which is passed over a frictionless light pulley,and the other end of the rope is tied to a weight of mass which is half of that of the (bucket $+$ water). The water pressure above atmospheric pressure at the bottom is ....... $kPa$.

$A$ balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it,its radius changes from $R$ to $0$ in time $T$. If the speed $\psi(r)$ of gas coming out of the balloon depends on $r$ as $r^\alpha$ and $T \propto S^a A^\beta \rho^\gamma R^\delta$,then:

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $5r/4$ (the pressure of the atmosphere is equal to the $10 \, m$ height of water column). If the temperature is constant and the surface tension is neglected,the depth of the lake is .... $m$ (in $.53$)

Two vessels of equal cross-sectional area $A$ are filled with a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and in the other vessel is $h_2$. When both vessels are connected,find the work done by gravity.

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes $5$ times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is (The temperature of the water in the lake is same at all points). (in $H$)