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

Option: 1
$3 \mathrm{~F} / 2$

Option: 2
$3 \mathrm{~F} / 4$

Option: 3
$\mathrm{F}$

Option: 4
$2 \mathrm{~F}$

Answers (1)

best_answer

Condition 1:

$\mathrm{F=\frac{KQ^{2}}{r^{2}}}$

Condition 2:

Force experienced by c is

$\mathrm{F^{\prime} =F_B-F_A }$

$\mathrm{=\frac{K(3 Q / 4)^2}{(r / 2)^2}-\frac{K\left(\frac{3 Q}{4}\right)(Q / 2)}{(r / 2)^2} }$

$\mathrm{=\frac{9 K Q^2}{4 r^2}-\frac{3 K Q^2}{2 r^2} }$

$\mathrm{F^{\prime} =\frac{3 K Q^2}{4 r^2}=\frac{3}{4} \mathrm{~F}}$

Hence 2 is correct option

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Anam Khan

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