A rod of length $$60 \mathrm{~cm}$$ rotates with a uniform angular velocity $$20 \mathrm{~rad} \mathrm{s}^{-1}$$ about its perpendicular bisector, in a uniform magnetic filed $$0.5 T$$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _________ V.

The disintegration energy $$Q$$ for the nuclear fission of $${ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n$$ is _______ $$\mathrm{MeV}$$.

Given atomic masses of $${ }^{235} \mathrm{U}: 235.0439 u ;{ }^{140} \mathrm{Ce}: 139.9054 u, { }^{94} \mathrm{Zr}: 93.9063 u ; n: 1.0086 u$$, Value of $$c^2=931 \mathrm{~MeV} / \mathrm{u}$$.

Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})$$

A light ray is incident on a glass slab of thickness $$4 \sqrt{3} \mathrm{~cm}$$ and refractive index $$\sqrt{2}$$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ $$\mathrm{cm}$$.

(Given $$\sin 15^{\circ}=0.25$$)