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+1 vote
34.1k views
in Physics by (49.1k points)

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is 

(1) 1 

(2) √2 

(3) 2 

(4) 1/√2

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2 Answers

+2 votes
by (46.9k points)

Answer is (4) 1/√2

+1 vote
by (20 points)

The correct answer is (4)\({1\over\sqrt2}\) .

Answer 1:
\(v_{o}=\sqrt{\dfrac{GM}{R}}\)...........(1)

\(v_{e}=\sqrt{\dfrac{2GM}{R}}\)..........(2)

Dividing equation (1) by (2), we get,

\(\dfrac{v_{o}}{v_{e}}=\dfrac{1}{\sqrt{2}}\)

Answer 2:

\(v_{o} <v_{e}\) as orbit radius is R.

\(\dfrac{v_o}{v_{e}} <1\)

Eliminating all other options which are \(\geq 1\),we get,

\(\dfrac{v_{o}}{v_{e}}=\dfrac{1}{\sqrt{2}}\)

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