Two equal sphere each weighting 1g hang by 2 equal silk thread from the same point the sphere are charged with in Contact and comes to rest with their centre 2 cm apart and 20 cm vertically below the point of support .find charge on sphere? solutions of this question

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Answer
Figure shows forces acting on charged sphere. Weight mg is acting downward. Repulsive electrostatic force is shown as Fe .

Tension force T acting along string is resolved as ( T cosθ ) and ( T sinθ ) .

(Tcosθ) component balances weight mg. (T sinθ) component balances Electrostatic force Fe .

T cosθ = mg ...................... (1)

T sinθ = Fe ........................(2)

If we eliminate tension T in above equations, we get , Fe = m g tanθ .......................(3)

Eqn.(3) is written as

K × ( q2 / d2 ) = ( m g tanθ ) ........................... (4)

where K = 1/( 4 π εo ) = 9 × 109 N m2 C-2 Coulomb's constant and d = 2 cm is the distance between charged spheres.

m is mass of sphere , g is acceleration due to gravity and θ is the angle made by the string with vertical

Solve this if you have a brain
We are given that each sphere weighs 1g, so their combined weight is 2g or 0.002kg. The distance between their centers is 2cm or 0.02m. We need to find the charge on each sphere.

From equation (1), we have:

T cosθ = mg

Since the spheres are hanging vertically, θ = 90° and cosθ = 0. Substituting values, we get:

T * 0 = 0.002 * 9.8
T = 0

This means there is no tension in the silk threads holding the spheres.

From equation (2), we have:

T sinθ = Fe

Substituting values, we get:

T * 1 = Fe

Fe = T

But we just found that T = 0, so Fe = 0 as well. This means there is no electrostatic force between the spheres, and they must be neutral (i.e. have no charge).

Therefore, the charge on each sphere is 0.