JEE Mains · Physics · STD 11 - 7. gravitation
The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\)
- A \(40\)
- B \(36\)
- C \(30\)
- D \(25\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
\(T =\frac{2 \pi}{\sqrt{ GM }} r ^{3 / 2}\) \(\frac{ T _{1}}{ T _{2}}=\left(\frac{ r _{1}}{ r _{2}}\right)^{3 / 2}=\left(\frac{1}{3}\right)^{3 / 2}\) \(T _{2}= T _{1} 3 \sqrt{3}=21 \sqrt{3} \,\text { hours }\) \(\approx 36 \,\text { hours }\)
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