two identical pith balls each of mass 10 mg is suspended from a fixed point by string length of 0.5 when each ball is given a charge Q the repellent came to equilibrium each train making an angle of 30 degree with the vertical on the charge q and the tension in the string
To find the tension in the string and the charge on each pith ball, we can use the principles of electrostatics and considering the equilibrium condition.
Given:
- Mass of each pith ball: 10 mg (0.01 g)
- String length: 0.5 m
- Angle made by the string with the vertical: 30 degrees
Step 1: Find the weight of each pith ball.
The weight of each pith ball can be calculated using the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
We know the mass of each pith ball is 10 mg, which is 0.01 g. The gravitational acceleration (g) is approximately 9.8 m/s².
Weight of each pith ball = 0.01 g * 9.8 m/s² = 0.098 N
Step 2: Find the tension in the string.
In the equilibrium condition, the tension in the string is equal to the weight of each pith ball.
Tension in the string = Weight of each pith ball = 0.098 N
Step 3: Find the charge on each pith ball.
To find the charge on each pith ball, we need to know that the electrostatic force of repulsion between the pith balls is equal to the weight of each ball.
Electrostatic force (Fe) = Weight of each pith ball = 0.098 N
The electrostatic force of repulsion can be calculated using the formula:
Fe = (k * q1 * q2) / r²
Where:
- k is the electrostatic constant (9 x 10^9 N m²/C²)
- q1 and q2 are the charges on the pith balls
- r is the separation between the charges, which is double the string length (2 * 0.5 m = 1 m)
Plugging in the values, we have:
0.098 N = (9 x 10^9 N m²/C²) * q * q / (1 m)²
Simplifying the equation, we get:
0.098 N = (9 x 10^9 N m²/C²) * q²
Divide both sides by (9 x 10^9 N m²/C²):
0.098 N / (9 x 10^9 N m²/C²) = q²
Now, take the square root of both sides:
q = √(0.098 N / (9 x 10^9 N m²/C²))
Calculating the value of q, we find:
q ≈ 8.25 x 10^(-8) C
So, the charge on each pith ball is approximately 8.25 x 10^(-8) C.
To summarize:
- Tension in the string: 0.098 N
- Charge on each pith ball: 8.25 x 10^(-8) C