A block is fastened to a horizontal spring. The block is pulled to a distance $$x=10 \mathrm{~cm}$$ from its equilibrium position (at $$x=0$$) on a frictionless surface from rest. The energy of the block at $$x=5$$ $$\mathrm{cm}$$ is $$0.25 \mathrm{~J}$$. The spring constant of the spring is ___________ $$\mathrm{Nm}^{-1}$$

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $$t=10 \mu \mathrm{m}$$ and refractive index $$\mu=1.2$$ is inserted infront of slit $$S_{1}$$. The experiment is conducted in air $$(\mu=1)$$ and uses a monochromatic light of wavelength $$\lambda=500 \mathrm{~nm}$$. Due to the insertion of the plate, central maxima is shifted by a distance of $$x \beta_{0} . \beta_{0}$$ is the fringe-width befor the insertion of the plate. The value of the $$x$$ is _____________.

Nucleus A having $$Z=17$$ and equal number of protons and neutrons has $$1.2 ~\mathrm{MeV}$$ binding energy per nucleon.

Another nucleus $$\mathrm{B}$$ of $$Z=12$$ has total 26 nucleons and $$1.8 ~\mathrm{MeV}$$ binding energy per nucleons.

The difference of binding energy of $$\mathrm{B}$$ and $$\mathrm{A}$$ will be _____________ $$\mathrm{MeV}$$.

Moment of inertia of a disc of mass '$$M$$' and radius '$$R$$' about any of its diameter is $$\frac{M R^{2}}{4}$$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $$\frac{x}{2}$$ MR$$^{2}$$. The value of $$x$$ is ___________.