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 _____________ $$\times 10^{-5}$$

Two identical circular wires of radius $$20 \mathrm{~cm}$$ and carrying current $$\sqrt{2} \mathrm{~A}$$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ $$\times 10^{-8} \mathrm{~T}$$.

(Take $$\pi=3.14$$)

A pole is vertically submerged in swimming pool, such that it gives a length of shadow $$2.15 \mathrm{~m}$$ within water when sunlight is incident at angle of $$30^{\circ}$$ with the surface of water. If swimming pool is filled to a height of $$1.5 \mathrm{~m}$$, then the height of the pole above the water surface in centimeters is $$\left(n_{w}=4 / 3\right)$$ ____________.

A particle of mass $$10 \mathrm{~g}$$ moves in a straight line with retardation $$2 x$$, where $$x$$ is the displacement in SI units. Its loss of kinetic energy for above displacement is $$\left(\frac{10}{x}\right)^{-n}$$ J. The value of $$\mathrm{n}$$ will be __________