Imagine a light planet revolving around a very massive star in a circular orbit of radius .r. with a period of revolution T. On what power of r will the square of time period depend if the gravitational force of attraction between the planet and the star is proportional to r^(-5//2)

Imagine a light planet revolving around a very massive star in a circu

1.	Imagine a light planet revolving around a very massive star in a circular orbit of radius .r. with a period of revolution T. On what power of r will the square of time period depend if the gravitational force of attraction between the planet and the star is proportional to r^(-5//2)
Answer» <html><body><p></p>Solution :Here <a href="https://interviewquestions.tuteehub.com/tag/gravitational-476409" style="font-weight:bold;" target="_blank" title="Click to know more about GRAVITATIONAL">GRAVITATIONAL</a> force <a href="https://interviewquestions.tuteehub.com/tag/provides-1171126" style="font-weight:bold;" target="_blank" title="Click to know more about PROVIDES">PROVIDES</a> centripetal force,<br/>`(mv^2)/( r) = (<a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a>)/(r^(5//2)) rArr <a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>^2 = (K)/(<a href="https://interviewquestions.tuteehub.com/tag/mr-549185" style="font-weight:bold;" target="_blank" title="Click to know more about MR">MR</a>^(3//2)) rArr T = (2pi r)/(v) = 2pi r sqrt((mr^(3//2))/(K)) rArr T^2 prop r^(7//2)`</body></html>