Question

Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is : 

(1) 4 N 

(2) 6 N 

(3) 1 N 

(4) 12 N

Answer 1

Correct option is : (2) 6 N 

\(\mathrm{F}_{\mathrm{PS}} \propto \mathrm{Q}^{2}\)

\(\mathrm{F}_{\mathrm{PS}}=16 \mathrm{~N}\) 

Now If P & R are brought in contact then 

Now If S & R are brought in contact then

New force between P & S is :

\(\mathrm{F}_{\mathrm{PS}} \propto \frac{\mathrm{Q}}{2} \times \frac{3 \mathrm{Q}}{4}\)

\(\mathrm{F}_{\mathrm{PS}} \propto \frac{3 \mathrm{Q}^{2}}{8}=\frac{3}{8} \times 16=6 \mathrm{N}\)