Question

Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be

• A. \(\frac{3}{2}F\)
• B. \(\frac{3}{4}F\)
• C. F
• D. 2F

Answer 1

The Correct Option is B

When two identical sphere come in contact with each other, the total charge on them is equally distribute.

\(\frac{kQ^2}{d^2}\)=F

F=\(\frac{k9Q^2}{16×\frac{d^2}{4}}−\frac{k3Q^2}{8×\frac{d^2}{4}}\)
=\(\frac{9kQ^2}{4d^2}−\frac{3kQ^2}{2d^2}\)
=\(\frac{kQ^2}{d^2}[\frac{9}{4}−\frac{3}{2}]\)
=\(\frac{6}{8}F\)
=\(\frac{3}{4}F\)
So, the correct option is (B): \(\frac{3}{4}F\)