SATHEE: Gravitation Question 351

Gravitation Question 351

Question: A satellite of mass m is orbiting the earth in a circular orbit of radius R. It starts losing energy due to small air resistance at the rate of C J/s. Find the time taken for the satellite to reach the earth.

Options:

A) $[\frac{G M m}{C} [\frac{1}{R} - \frac{1}{r}]]$

B) $[\frac{G M m}{2 C} [\frac{1}{R} + \frac{1}{r}]]$

C) $[\frac{G M m}{2 C} [\frac{1}{R} - \frac{1}{r}]]$

D) $[\frac{2 G M m}{C} [\frac{1}{R} + \frac{1}{r}]]$

Show Answer

Answer:

Correct Answer: C

Solution:

$[E = - \frac{G M m}{2 r}]$ $[- \frac{d E}{d t} = \frac{G M m}{2 r} \frac{1}{r^{2}} \frac{d r}{d t}]$

$[\int_{0}^{t} d t = - \frac{G M m}{2 C} \int_{r}^{R} \frac{d r}{r^{2}}; t = \frac{G M m}{2 C} [\frac{1}{R} - \frac{1}{r}]]$

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Gravitation Question 351

Question: A satellite of mass m is orbiting the earth in a circular orbit of radius R. It starts losing energy due to small air resistance at the rate of C J/s. Find the time taken for the satellite to reach the earth.

Options:

Answer:

Solution:

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