Question

two identical particles each of having a charge of 10 microcoulomb are tied with two string of equal length one metre at a common point if both the string makes an angle of 30 degree with vertical then mass of each particle will be​

Answer 1

see diagram,

free body diagram of particles is shown clearly.

at equilibrium,

upward force = downward force

Tcos30° = mg ........(1)

backward force = forward force

Tsin30° = Fe = kq²/r² ......(2)

where r = 2lsin30° , where l = length of string.

from equation (1) and (2),

tan30° = kq²/r²mg

or, 1/√3 = kq²/(2lsin30°)²mg

or, m = √3kq²/4l²sin²30g

here, k = 9 × 10^9 Nm²/C² , q = 10^-5 , l = 1m and g = 10m/s²

so, m = √3 × 9 × 10^9 × (10^-5)²/{4 × 1 × (1/2)² × 10}

= 9√3 × 10^-1/{10}

= 9√3/100

= 15.588/100

= 0.15588 kg≈ 0.15 kg