SATHEE: Gravitation Question 208

Gravitation Question 208

Question: The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as [AMU 1995]

Options:

A) $[4 π^{2} R^{3} G^{- 1} T^{- 2}]$

B) $[8 π^{2} R^{3} G^{- 1} T^{- 2}]$

C) $[12 π^{2} R^{3} G^{- 1} T^{- 2}]$

D) $[16 π^{2} R^{3} G^{- 1} T^{- 2}]$

Show Answer

Answer:

Correct Answer: A

Solution:

$[m ω^{2} R = \frac{G M m}{R^{2}}, \Rightarrow, {(\frac{2 π}{T})}^{2} R = \frac{G M}{R^{2}}]$ $[\Rightarrow, M = \frac{4 π^{2} R^{3}}{G T^{2}}]$

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Gravitation Question 208

Question: The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as [AMU 1995]

Options:

Answer:

Solution:

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