If $$\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m}$$ and $$\vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}$$. The magnitude of component of vector $$\vec{A}$$ along vector $$\vec{B}$$ will be ____________ $$\mathrm{m}$$.

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ___________ $$\mathrm{m}$$.

Given, the length of the rod is $$10 \sqrt{3} \mathrm{~m}$$.

In the given figure, the face $$A C$$ of the equilateral prism is immersed in a liquid of refractive index '$$n$$'. For incident angle $$60^{\circ}$$ at the side $$A C$$, the refractive light beam just grazes along face $$A C$$. The refractive index of the liquid $$n=\frac{\sqrt{x}}{4}$$. The value of $$x$$ is ____________.

(Given refractive index of glass $$=1.5$$ )

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :

$${ }_{1}^{2} X+{ }_{1}^{2} X={ }_{2}^{4} Y$$

The binding energies per nucleon for $$\frac{2}{1} X$$ and $${ }_{2}^{4} Y$$ are $$1.1 \,\mathrm{MeV}$$ and $$7.6 \,\mathrm{MeV}$$ respectively. The energy released in this process is _______________ $$\mathrm{MeV}$$.