Question

A satellite of mass $m$ revolves around the earth of mass $M$ in a circular orbit of radius $r$ , with an angular velocity $\omega$. If the radius of the orbit becomes $9r$ , then angular velocity of this orbit becomes

• A. $9\omega$
• B. $\frac{\omega }{9}$
• C. $27\omega$
• D. $\frac{\omega }{27}$

Answer 1

The correct option is D $\frac{\omega }{27}$

$\frac{GMm}{r^2}=m{\omega }^{2}r$ $[\because$ Attraction force=Centripetal Force $]$

Similarly,

$\frac{Gmm}{(9r{)}^2}=m{\omega }_1^{2}9r$

$\frac{m{\omega }^{2}r}{81}=m{\omega }_1^{2}r9$

${\omega }_1=\frac{\omega }{27}$