Explanation

(c) Cathode rays are composed of electrons, when they move in electric field a force
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F = eE\ \ \ \ $…(i)
Acts on them, this provides the necessary centripetal force to the particles
$F = \frac{mv^{2}}{r}\ \ \ $…(ii)
From Eqs. (i) and (ii), we get
$eE = \frac{mv^{2}}{r}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r = \frac{mv^{2}}{eE} = \frac{m\left( 10^{6} \right)^{2}}{e(300)}\ \ \ \ \ $…(iii)
When velocity is doubled same circular path is followed, hence radius is same
$r = \frac{m\left( 2 \times 10^{6} \right)^{2}}{eE}\ \ \ $…(iv)
Equating Eqs. (iii) and (iv), we get
$m \times \frac{\left( 10^{6} \right)^{2}}{300e} = \frac{m \times \left( 2 \times 10^{6} \right)^{2}}{eE}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E = 300 \times 4 = 1200$ V-$cm^{- 1}$