Question

Two small identical spheres having charges $+10\text{μC}$ and $-90\text{μC}$ attract each other with a force of $F$ newton. If they are kept in contact and then separated by the same distance, the new force between them is -

• A. $\frac{F}{6}$
• B. $16F$
• C. $\frac{16F}{9}$
• D. $9F$

Answer 1

Answer: (C)

$F=\frac{k\left(10\right)\left(90\right)}{r^2}\dots \dots ..\left(i\right)$
charge on each when contact is made
$q_1\prime =q_2\prime =\frac{10+\left(-90\right)}{2}=-40\mu C$
$\therefore$ New force $F^{\prime }=\frac{k\left(40\right)\left(40\right)}{r^2}$
$\therefore \frac{\text{F}\prime }{F}=\frac{40\times 40}{10\times 90}=\frac{16}{9}$
$\therefore F^{\prime }=\frac{16}{9}F$