At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average speed in the gas. Then, the value of $$\alpha$$ will be

(used $$\pi = {{22} \over 7}$$)

A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

A particle of mass 100 g is projected at time t = 0 with a speed 20 ms$$^{-1}$$ at an angle 45$$^\circ$$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2s is found to be $$\mathrm{\sqrt K~kg~m^2/s}$$. The value of K is ___________.

(Take g = 10 ms$$^{-2}$$)

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 20 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $$\frac{x}{10}\times10^{-3}$$, where $$x$$ is ___________