Question

Two pith balls, each of mass 1.8 g, are suspended from the same point by silk threads each of length 20 cm. When equal charge Q is given to both the balls, they separate until the two threads become perpendicular. Then the charge Q on each pith ball is ______.

Note: `[1/(4piepsilon_0) = 9 xx 10^9)]`nm²/c² 

Options

• 2 × 10^-7 C 

• 3 × 10^-7 C

• 4 × 10^-7 C 

• 5 × 10^-7 C

Answer 1

Two pith balls, each of mass 1.8 g, are suspended from the same point by silk threads each of length 20 cm. When equal charge Q is given to both the balls, they separate until the two threads become perpendicular. Then the charge Q on each pith ball is 4 × 10^-7 C.

Explanation:

T cos 45 = mg    ...(i)

T sin 45 = `"kq"^2/"mgr"^2`   ...(ii)

(r = 2 l sin 45°) & k = 9 × 10⁹

From (i) & (ii)

`tan 45^circ = "kq"^2/"mgr"^2`

`=> "q" = sqrt("mg r"^2  tan 45^circ)/"k"`

putting values of m, g, k, r we get q = 4 × 10^-7 C