A hydraulic lift as shown in the figure is used to lift a mass of 1000 kg , which is placed on a piston $\left(P_1\right)$ of area $1 \mathrm{~m}^2$. If the cross-section area of the piston $\left(P_2\right)$ at the other end is $0.01 \mathrm{~m}^2$, then how much mass needs to be put on it to lift the 1000 kg ?

The change in surface energy when a big spherical drop fo radius $R$ is split into $n$ spherical droplets of radius $r$ is ( $T=$ surface tension)

A block of iron contains a hollow cavity as shown below. The block weighs 6000 N in air and 4000 N in water. If the density of iron and water are $6 \mathrm{~g} / \mathrm{cm}^3$ and $1 \mathrm{~g} / \mathrm{cm}^3$, then the volume of the cavity is (assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A cubical block of wood having mass of 160 g has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. Specific gravity of wood is 0.8 and that metal is 10 and density of water $=1 \mathrm{~g} / \mathrm{cc}$.