The density and breaking stress of a wire are $$6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$$ and $$1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{\text {rd }}$$ of the value on the surface of earth. The maximum length of the wire with breaking is _______ $$\mathrm{m}$$ (take, $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $$20 \mu \mathrm{F}$$ is __________ V.

A body moves on a frictionless plane starting from rest. If $$\mathrm{S_n}$$ is distance moved between $$\mathrm{t=n-1}$$ and $$\mathrm{t}=\mathrm{n}$$ and $$\mathrm{S}_{\mathrm{n}-1}$$ is distance moved between $$\mathrm{t}=\mathrm{n}-2$$ and $$\mathrm{t}=\mathrm{n}-1$$, then the ratio $$\frac{\mathrm{S}_{\mathrm{n}-1}}{\mathrm{~S}_{\mathrm{n}}}$$ is $$\left(1-\frac{2}{x}\right)$$ for $$\mathrm{n}=10$$. The value of $$x$$ is __________.

In Young's double slit experiment, carried out with light of wavelength $$5000~\mathop A\limits^o$$, the distance between the slits is $$0.3 \mathrm{~mm}$$ and the screen is at $$200 \mathrm{~cm}$$ from the slits. The central maximum is at $$x=0 \mathrm{~cm}$$. The value of $$x$$ for third maxima is __________ $$\mathrm{mm}$$.