A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $$9 \mathrm{~kg}$$ is suspended from the wire. When this mass is replaced by a mass $$\mathrm{M}$$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of '$$M$$' is

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

Water rises in a capillary tube of radius '$$r$$' up to a height '$$\mathrm{h}$$'. The mass of water in a capillary is '$$\mathrm{m}$$'. The mass of water that will rise in a capillary tube of radius $$\frac{'r'}{3}$$ will be

In a wheatstone's bridge, three resistances $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ are connected in the three arms and the fourth arm is formed by two resistances $$S_1$$ and $$S_2$$ connected in parallel. The condition for the bridge to be balanced is