A stationary object at $4^{\circ} \mathrm{C}$ and weighing 3.5 kg falls from a height of 2000 m on snow mountain at $0^{\circ} \mathrm{C}$. If the temperature of the object just before hitting the snow is $0^{\circ} \mathrm{C}$ and the object comes to rest immediately then the quantity of ice that melts is (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$, Latent heat of ice $=3.5 \times 10^5 \mathrm{~J} / \mathrm{kg}$ )

Six molecules of a gas in container have speeds $2 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}, 6 \mathrm{~m} / \mathrm{s}, 3 \mathrm{~m} / \mathrm{s}$, and $5 \mathrm{~m} / \mathrm{s}$. The r.m.s. speed is

During thermodynamic process, the increase in internal energy of a system is equal to the $\mathrm{w}_{0 r k}$ done on the system. Which process does the system undergo?

How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5 \%$ at the constant temperature?