Question

Two identical simple pendulums have different charges Q, and Q2 on their bobs. When they are
suspended from the same point, their strings make angle 0, and e, from the vertical as shown,
hence Q. Q
​

Answer 1

Given that,

First charge = Q₁

Second charge = Q₂

Angle =θ₁

Angle =θ₂

Suppose, They diverge and reach equilibrium with the strings of pendulums A and B making angles θ₁ and θ₂ with the vertical respectively.

We know that,

It doesn't matter which bob has more charge, the force acting between them will still be the same.

Thus they will make the same angle from the vertical.

We need to prove the the strings of pendulums A and B making angles θ₁ and θ₂ with the vertical

Using electrostatics force

$F=\dfrac{kq_{1}q_{2}}{r^2}$

Where, $q_{1}$ = first charge

$q_{2}$ = second charge

r = distance between both bobs

Put the value into the formula

$F=\dfrac{kQ_{1}\times Q_{2}}{r^2}$

According to figure,

The tension in first string is T₁ and the tension in second string is T₂.

The both tensions are equal.

$T_{1}=T_{2}$

Their strings make angle θ₁ and θ₂ from the vertical

So, $\theta_{1}=\theta_{2}$

Hence, This is the required solution.

Answer 2

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