A wire of density $$8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ is stretched between two clamps $$0.5 \mathrm{~m}$$ apart. The extension developed in the wire is $$3.2 \times 10^{-4} \mathrm{~m}$$. If $$Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$, the fundamental frequency of vibration in the wire will be ___________ $$\mathrm{Hz}$$.

The length of a wire becomes $$l_{1}$$ and $$l_{2}$$ when $$100 \mathrm{~N}$$ and $$120 \mathrm{~N}$$ tensions are applied respectively. If $$10 ~l_{2}=11~ l_{1}$$, the natural length of wire will be $$\frac{1}{x} ~l_{1}$$. Here the value of $$x$$ is _____________.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $$2.0 \mathrm{~cm}^{2}$$. The area of cross section at the outlet is $$10 \mathrm{~mm}^{2}$$. If the piston is pushed at a speed of $$4 \mathrm{~cm} \mathrm{~s}^{-1}$$, the speed of outgoing fluid is __________ $$\mathrm{cm} \mathrm{s}^{-1}$$

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $$\times$$ 10$$^{-6}$$ m. [Young's modulus for steel = 2 $$\times$$ 10$$^{11}$$ Nm$$^{-2}$$ and g = 10 ms$$^{-2}$$ ]