A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' $r$ ' $m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum, the radius ' r ' in m is $\left[\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right]\left[\mathrm{x}=2 \times 10^{-16}\right]$

A particle performing uniform circular motion of radius $\frac{\pi}{2} \mathrm{~m}$ makes $x$ revolutions in time $t$. Its tangential velocity is

The frequency of revolution of an electron in the $\mathrm{n}^{\text {th }}$ orbit of hydrogen atom is

The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2){ }^{\circ} \mathrm{C}$ and $(82.3 \pm 0.3){ }^{\circ} \mathrm{C}$. The rise in temperature with proper error limits is