Two identical small bodies each of mass m and charge q are suspended from two strings each of length l from a fixed point . This whole system is taken into an orbiting artificial satellites, then find the tension in strings a) kq^2/l^2+2mg b) kq^2/4l^2+ 2mg. c) kq^2/l^2 d) kq^2/4l^2 Correct option is (d) How to solve this question?

Question

Two identical small bodies each of mass m and charge q are suspended from two strings each of length l from a fixed point . This whole system is taken into an orbiting artificial satellites, then find the tension in strings                                      a) kq^2/l^2+2mg                         b) kq^2/4l^2+ 2mg.                     c) kq^2/l^2                                   d) kq^2/4l^2                           Correct option is (d) How to solve this question?

Answer

To find the tension in the strings, we need to consider the forces acting on the bodies.

1. Gravitational Force:
Each body experiences a gravitational force of magnitude mg, where m is the mass of the body and g is the acceleration due to gravity.

2. Electrostatic Force:
The bodies have charges q, so they experience an electrostatic force due to their charges. Since the bodies have the same charge and are identical, the electrostatic force between them will be attractive.

3. Centripetal Force:
When the system is taken into an orbiting artificial satellite, the bodies will experience a centripetal force due to their circular motion. This force is directed towards the center of the circular path.

Now let's analyze the forces acting on each body:

1. For the first body:
- Gravitational force: mg, directed downwards.
- Electrostatic force: Attractive force towards the other body.
- Tension in string: T1, directed upwards.

2. For the second body:
- Gravitational force: mg, directed downwards.
- Electrostatic force: Attractive force towards the other body.
- Tension in string: T2, directed upwards.

Since the bodies are in equilibrium, the net force acting on each body must be zero. Therefore, we can write the following equations:

For the first body:
T1 - mg - F_e = 0 (Equation 1)

For the second body:
T2 - mg - F_e = 0 (Equation 2)

where F_e is the electrostatic force between the bodies.

Now, let's consider the electrostatic force between the bodies. The electrostatic force can be calculated using Coulomb's Law:

F_e = (k * q^2) / l^2

where k is the electrostatic constant, q is the charge of each body, and l is the distance between them (which is equal to the length of each string).

Substituting this value of F_e into Equation 1 and Equation 2, we get:

T1 - mg - (k * q^2) / l^2 = 0 (Equation 3)
T2 - mg - (k * q^2) / l^2 = 0 (Equation 4)

Since the bodies are identical, the tensions in the strings will be equal. Therefore, T1 = T2 = T.

Combining Equation 3 and Equation 4, we get:

2T - 2mg - (k * q^2) / l^2 = 0

Simplifying this equation, we find:

2T = 2mg + (k * q^2) / l^2
T = mg + (k * q^2) / (2l^2)

Comparing this with the given options, we can see that the correct option is (d) kq^2/4l^2 2mg.

Answer

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