A wire of length $$\mathrm{L}$$ and radius $$\mathrm{r}$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$\mathrm{F}$$, its length increases by $$5 \mathrm{~cm}$$. Another wire of the same material of length $$4 \mathrm{L}$$ and radius $$4 \mathrm{r}$$ is pulled by a force $$4 \mathrm{F}$$ under same conditions. The increase in length of this wire is __________________ $$\mathrm{cm}$$.

The excess pressure inside a liquid drop is 500 Nm^{$$-$$2}. If the radius of the drop is 2 mm, the surface tension of liquid is x $$\times$$ 10^{$$-$$3} Nm^{$$-$$1}. The value of x is _____________.

A small spherical ball of radius 0.1 mm and density 10^{4} kg m^{$$-$$3} falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m.

(Given g = 10 ms^{$$-$$2}, viscosity of water = 1.0 $$\times$$ 10^{$$-$$5} N-sm^{$$-$$2}).

A liquid of density 750 kgm^{$$-$$3} flows smoothly through a horizontal pipe that tapers in cross-sectional area from A_{1} = 1.2 $$\times$$ 10^{$$-$$2} m^{2} to A_{2} = $${{{A_1}} \over 2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $$\times$$ 10^{$$-$$3} m^{3}s^{$$-$$1}.