A steel rod has a radius of $$20 \mathrm{~mm}$$ and a length of $$2.0 \mathrm{~m}$$. A force of $$62.8 ~\mathrm{kN}$$ stretches it along its length. Young's modulus of steel is $$2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$. The longitudinal strain produced in the wire is _____________ $$\times 10^{-5}$$

The surface of water in a water tank of cross section area $$750 \mathrm{~cm}^{2}$$ on the top of a house is $$h \mathrm{~m}$$ above the tap level. The speed of water coming out through the tap of cross section area $$500 \mathrm{~mm}^{2}$$ is $$30 \mathrm{~cm} / \mathrm{s}$$. At that instant, $$\frac{d h}{d t}$$ is $$x \times 10^{-3} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ will be ____________.

A certain pressure '$$\mathrm{P}$$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $$0.01 \%$$ whereas the liquid gets compressed to $$0.03 \%$$. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is ____________.

A thin rod having a length of $$1 \mathrm{~m}$$ and area of cross-section $$3 \times 10^{-6} \mathrm{~m}^{2}$$ is suspended vertically from one end. The rod is cooled from $$210^{\circ} \mathrm{C}$$ to $$160^{\circ} \mathrm{C}$$. After cooling, a mass $$\mathrm{M}$$ is attached at the lower end of the rod such that the length of rod again becomes $$1 \mathrm{~m}$$. Young's modulus and coefficient of linear expansion of the rod are $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$ and $$2 \times 10^{-5} \mathrm{~K}^{-1}$$, respectively. The value of $$\mathrm{M}$$ is __________ $$\mathrm{kg}$$.

(Take $$\mathrm{g=10~m~s^{-2}}$$)