Question

If mass of planet revolving around the sun is doubled and its frequency remains constant then radius of its orbit will be

Answer 1

Answer:

earth revolving around the sun is doubled and its frequency

Answer 2

The radius of its orbit will be (2)1/3 radius of the planet.

Explanation:

The time peroid of the planet revolving around sun is given as

$T=\frac{4\pi^2r^3}{GM}$

Here M is the mass of the planet and r is the radius and G is the gravitional constant.

Frequency is the reciprocal of time period. so if frequency remains constant then time period will be also constant.

If mass is doubled and time period remain same then, radius of the orbit will be

$T=\frac{4\pi^2r^`^3}{G2M}$

dividing bothe equation, we get

$\frac{T}{T} =\frac{\frac{4\pi^2r^3}{GM}}{\frac{4\pi^2r^`^3}{G2M}}$

$r^` = (2)^\frac{1}{3} r$

Thus, the radius of its orbit will be (2)1/3 radius of the planet.

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