Question

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become:

• A. 10 hours
• B. 80 hours
• C. 40 hours
• D. 20 hours

Hint:

If distance increases by factor $n$, time period increases by $n\sqrt{n}$.

Answer 1

The Correct Option is C

Step 1: Concept
According to Kepler's Third Law, $T^{2} \propto R^{3}$.
Step 2: Analysis
$\frac{T_{2}}{T_{1}} = \left(\frac{R_{2}}{R_{1}}\right)^{3/2}$. Given $R_{2} = 4R_{1}$ and $T_{1} = 5$ hours. $T_{2} = 5 \times (4)^{3/2} = 5 \times 8$.
Step 3: Conclusion
The new time period $T_{2} = 40$ hours.
Final Answer: (C)