Question

a) Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Find their acceleration. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?

Answer 1

Explanation:

Given that,

Mass of the raindrops, $m=0.5\ g=0.0005\ kg$

Charges, $q=1\ mC=10^{-3}\ C$

Distance between raindrops, d = 1 cm = 0.01 m

(a) The force due to motion of raindrop is balanced by the electric force between charges. It is given by :

$ma=\dfrac{kq^2}{r^2}$

a is the acceleration of the raindrop

$a=\dfrac{kq^2}{r^2m}$

$a=\dfrac{9\times 10^9\times (10^{-3})^2}{(0.01)^2\times 0.0005}$

$a=1.8\times 10^{11}\ m/s^2$

(b) It is clear that the acceleration is too large. It can break apart the rain drop.

(c) If the charge is of the factor of $10^{-8}\ C$, the charge would be more reasonable.            

Hence, this is the required solution.