Question

10) Calculate the charge on each of a pair of pith balls suspended in air from the
same point by strings 0.1 m long if they repel each other to a separation of 0.1 m.
Mass of each pith ball is 100 mg.
Ans: CHARGE = 2.51 x 10-8 C​

Answer 1

charge on each pith ball is 2.51 × 10^-8 C

given, length of string , l = 0.1 m

seperation between pith balls , x = 0.1 m

angle made by a string of pith ball and vertical line is θ.

sinθ = (x/2)/l = x/2l = 0.1/0.2 = 1/2 = sin30°

so, θ = 30°

now Tcosθ = mg .......(1)

Tsinθ = Kq²/x² .........(2)

from equations (1) and (2) we get,

tanθ = Kq²/x²mg

⇒tan30° = 9 × 10^9 × q²/{(0.1)² × (100 × 10^-6kg) × 10 m/s²}

⇒1/√3 = 9 × 10^9 × q²/(10^-5)

⇒q² = 10^-14/(9√3) = (100/9√3) × 10^-16

⇒q = 2.51 × 10^-8 C

hence charge on each pith ball is 2.51 × 10^-8 C

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

given, length of string , l = 0.1 m

seperation between pith balls , x = 0.1 m

angle made by a string of pith ball and vertical line is θ.

sinθ = (x/2)/l = x/2l = 0.1/0.2 = 1/2 = sin30°

so, θ = 30°

now Tcosθ = mg .......(1)

Tsinθ = Kq²/x² .........(2)

from equations (1) and (2) we get,

tanθ = Kq²/x²mg

⇒tan30° = 9 × 10^9 × q²/{(0.1)² × (100 × 10^-6kg) × 10 m/s²}

⇒1/√3 = 9 × 10^9 × q²/(10^-5)

⇒q² = 10^-14/(9√3) = (100/9√3) × 10^-16

⇒q = 2.51 × 10^-8 C

hence charge on each pith ball is 2.51 × 10^-8 C