Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
Two identical pith balls, each with a charge q , are suspended from a common point using two strings of equal length l . Determine the mass of each ball given that the angle between the strings is 2 in equilibrium.
Options
- Aq^2 4 ₀ g l^2 ^2
- Bq^2 4 ₀ g l^2 ^2
- Cq^2 16 ₀ g l^2 ^2
- Dq^2 16 ₀ g l^2 ^2
Correct answer
C. q^2 16 ₀ g l^2 ^2
Step-by-step solution
The angle made by each string with the vertical is . Distance between the two balls, r = 2l . Electrostatic force of repulsion between the balls, F_e = 1 4 ₀ q^2 r^2 = q^2 16 ₀ l^2 ^2 . For the equilibrium of each ball, balancing the forces in the horizontal and vertical directions: T = F_e T = mg Dividing the two equations: = F_e mg m = F_e g = F_e g Substituting the value of F_e : m = q^2 16 ₀ g l^2 ^2