SATHEE: Gravitation Question 346

Gravitation Question 346

Question: An artificial satellite is first taken to a height equal to half the radius of earth. Assume that it is at rest on the earth’s surface initially and that it is at rest at this height. Let $[E_{1}]$ be the energy required. It is then given the appropriate orbital speed such that it goes in a circular orbit at that height. Let E be the energy required. The ratio $[\frac{E_{1}}{E_{2}}]$ is

Options:

A) 4:1

B) 3:1

C) 1:1

D) 1:2

Show Answer

Answer:

Correct Answer: C

Solution:

$[E_{1} = - \frac{G M_{e} m}{R_{e} + \frac{R_{e}}{2}} (- \frac{G M_{e} m}{R_{e}}) = \frac{G M_{e} m}{3 R_{e}}]$ $[E_{2} = \frac{1}{2} m v_{0}^{2} = \frac{1}{2} m . \frac{G M_{e}}{R_{e} + \frac{R_{e}}{2}} = \frac{G M_{e} m}{3 R_{e}}]$

$[∴ \frac{E_{1}}{E_{2}} = 1 : 1]$

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Gravitation Question 346

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