Tension in Strings Inside Orbiting Satellite

❓ 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.

If the whole system is taken into an orbiting artificial satellite, then find the tension in the strings.

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🖼 Question Image

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✍️ Short Explanation

This problem is based on:

👉 Artificial satellite conditions
👉 Weightlessness
👉 Electrostatic force and tension balance.

Main idea:

Inside orbiting satellite:

$$g_{effective}=0$$

So only electrostatic repulsion provides tension.

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🔷 Step 1 — Effect Inside Satellite 💯

In orbiting artificial satellite:

$$\text{Effective gravity}=0$$

Hence:

$$mg \text{ effect disappears}$$

So strings no longer balance weight.

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🔷 Step 2 — Forces on Charges

Both charges are identical:

$$q \text{ and } q$$

They repel each other.

Electrostatic force:

$$F=\frac{Kq^2}{r^2}$$

From geometry, distance between charges becomes:

$$r=2l$$

because strings become horizontal.

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🔷 Step 3 — Calculate Electrostatic Force

$$F=\frac{Kq^2}{(2l)^2}$$
$$F=\frac{Kq^2}{4l^2}$$

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🔷 Step 4 — Tension in String

In equilibrium:

$$T=F$$

Therefore:

$$T=\frac{Kq^2}{4l^2}$$

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🔷 Step 5 — Final Answer

$$\boxed{\frac{Kq^2}{4l^2}}$$

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🔷 Step 6 — JEE Trap Alert 🚨

❌ $mg$ include kar lena

❌ Distance between charges $=l$ assume kar lena

❌ Artificial satellite mein gravity zero effect bhool jaana

Remember:

In orbiting satellite:

$$\text{Apparent weight}=0$$

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✅ Final Answer

$$\boxed{\frac{Kq^2}{4l^2}}$$

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