A metallic surface is illuminated with radiation of wavelength $$\lambda$$, the stopping potential is $$V_{0}$$. If the same surface is illuminated with radiation of wavelength $$2 \lambda$$. the stopping potential becomes $$\frac{V_{o}}{4}$$. The threshold wavelength for this metallic surface will be

The free space inside a current carrying toroid is filled with a material of susceptibility $$2 \times 10^{-2}$$. The percentage increase in the value of magnetic field inside the toroid will be

From the $$\mathrm{v}-t$$ graph shown, the ratio of distance to displacement in $$25 \mathrm{~s}$$ of motion is:

A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at $$4 \mathrm{~km}$$ distance from it is $$x \times 10^{-2} \mathrm{~m}$$. The value of $$x$$ is __________.

(Let, radius of earth $$\mathrm{R}=6400 \mathrm{~km}$$ )