Question

A shower of protons from outer space deposits equal charges $+q$ on the earth and the moon when electrostatic repulsion exactly counterbalances the gravitational attraction. How large is $q$ ?

• A. $\sqrt{\frac{4\pi {ϵ}_{0}G}{M_e{M}_m}}$
• B. $\sqrt{\frac{GMm}{k}}$
• C. $\sqrt{\frac{G{M}_e{M}_m}{4\pi {ϵ}_0}}$
• D. $\sqrt{\frac{M_e{M}_m}{4\pi {ϵ}_{0}G}}$

Answer 1

The correct option is B $\sqrt{\frac{GMm}{k}}$

Mass of Earth $=Mkg$

Mass of Moon $=mkg$

Distance between them $=rkm$

Gravitational Attraction $F=\frac{{GM}_m}{r^2}$

Charge is $+q$

Electrostatic repulsion force $F^1=h\frac{q\times q}{r^2}$

As both forces counter balances each other $F=F^1$

$\frac{{GM}_m}{r^2}=k\frac{q\times q}{r^2}$

$\Rightarrow {GM}_m=k{q}^2$

$\Rightarrow q^2=\frac{{GM}_m}{k}$

$q=\sqrt{\frac{{GM}_m}{k}}$ units.