Explanation

(a)
Given, velocity of particle $A$=0.05 $ms^{- 1}$
Velocity of particle $B$=0.02 $ms^{- 1}$
Let the mass of particle $A = x$
∴ The mass of particle $B = 5x$
de-Broglie’s equation is
$\lambda = \frac{h}{mv}$
For particle $A$
$\lambda_{A} = \frac{h}{x \times 0.05}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
For particle $B$
$\lambda_{B} = \frac{h}{5x \times 0.02}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
Eq. (i)/(ii)
$\frac{\lambda_{A}}{\lambda_{B}} = \frac{5x \times 0.02}{x \times 0.05}$
$\frac{\lambda_{A}}{\lambda_{B}} = \frac{2}{1}$
or $2:1$