Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is__________

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$. Moment of intertia of the wheel is___________ $\mathrm{kg} \mathrm{}\,\, \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )