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

A metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of metallic is $10$. The tension in the string is ........  $N$

A small wooden ball of density $ \rho$ is immersed in water of density $\sigma $ to depth $h $ and then released. The height $H$ above the surface of water up to which the ball will jump out of water is

A hollow sphere has inner volume half the outer volume. Its $4/5\,th$ part is submerged when placed in water. The density of material is

A wide bottom cylindrical massless plastic container of height $9 \,cm$ has $40$ identical coins inside it and is floating on water with $3 \,cm$ inside the water. If we start putting more of such coins on its lid, it is observed that after $N$ coins are put, its equilibrium changes from stable to unstable. Equilibrium in floating is stable if the geometric centre of the submerged portion is above the centre of the mass of the object). The value of $N$ is closed to

Write the law of floatation and describe its cases.