The spring balance $A$ reads $2 \mathrm{kg}$ with a block $m$ suspended from it. A balance $B$ reads $5 \mathrm{kg}$ when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation

A jar is filled with two non-mixing liquids $1$ and $2$ having densities ${\rho }_1$ and ${\rho }_2$, respectively. A solid ball, made of a material of density ${\rho }_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho }_1$, ${\rho }_2$ and ${\rho }_3$?

A boat having a length $3 m$ and breadth $2 m$ is floating on a lake. The boat sinks by $1 cm$ when a man gets on it. The mass of the man is?

A wooden block, with a coin placed on its top, floats in water as shown in the figure. The distance $l$ and $h$ are shown there. After some time the coin falls into the water. Then

An iron bar (Young's modulus $={10}^{11} \mathrm{N} {\mathrm{m}}^{-2}, C={10}^{-6}º{\mathrm{C}}^{-1}$) $1 \mathrm{m}$ long and ${10}^{-3} {\mathrm{m}}^2$ in the area is treated from $0 {}^{\circ }\mathrm{C}$ to $100 {}^{\circ }\mathrm{C}$ without being allowed to bend or expand. Find the compressive force developed inside the bar.

A rod of length $2 \mathrm{m}$ rests on a smooth horizontal floor. If the rod is heated from $0°\mathrm{C} \text{to} 20°\mathrm{C}$, find the longitudinal strain developed ($\alpha =5\times {10}^{-5} °{\mathrm{C}}^{-1}$).