Two wires A and B are made of same material. Their diameters are in the ratio of $1: 2$ and lengths are in the ratio of $1: 3$. If they are stretched by the same force, then increase in their lengths will be in the ratio of
A horizontal pipe carries water in a streamlined flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^{-2}$, the velocity of water is $1 \mathrm{~ms}^{-1}$ and the pressure is 2000 Pa . What is the pressure of water at another point where the cross-sectional area is $5 \mathrm{~cm}^2$ ?
[Density of water $=1000 \mathrm{kgm}^{-3}$ ]
Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods, the temperature at the junction x is

A gas is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system along these two paths are $Q_1$ and $Q_2$ and $W_1$ and $W_2$ respectively. Then