An electron moves in a circular orbit with uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is [ $\mu_0=$ permeability of free space, $e=$ electronic charge]

If the maximum kinetic energy of emitted electrons in photoelectric effect is $3.2 \times 10^{-19} \mathrm{~J}$ and the work-function for metal is $6.63 \times 10^{-19} \mathrm{~J}$, then stopping potential and threshold wavelength respectively are

[Planck's constant, $h=6.63 \times 10^{34} \mathrm{~J}$-s]

[Velocity of light, $c=3 \times 10^8 \frac{\mathrm{~m}}{\mathrm{~s}}$ ]

[Charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ ]

The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Earth has mass $M_1$ and radius $R_1$. Moon has mass $M_2$ and radius $R_2$. Distance between their centre is $r$. A body of mass $M$ is placed on the line joining them at a distance $\frac{r}{3}$ from centre of the earth. To project the mass $M$ to escape to infinity, the minimum speed required is