First slide

Work done by Diff type of forces

Question

What is the radius of the circular orbit of a stationary satellite which remains motionless with respect to earth’s surface ?

Easy

A

${(\frac{{gR}^{2} T^{2}}{4 π^{2}})}^{\frac{1}{3}}$
B

${(\frac{gR}{4 π^{2} T^{2}})}^{\frac{1}{2}}$
C

${(\frac{gRT}{2 π})}^{\frac{1}{3}}$
D

${(\frac{gR}{2 πT})}^{\frac{1}{2}}$

Solution

A satellite will appear motionless when its period of revolution is the same as that of earth that is T=24 hours. Let r be the radius of orbit from the centre of earth. Then dynamics of circular motion
${mω}^{2} r = \frac{GMm}{r^{2}}; {(\frac{2 π}{T})}^{2} r^{3} = GM$
$r = {(\frac{{GMT}^{2}}{4 π^{2}})}^{\frac{1}{3}} = {(\frac{{gR}^{2} T^{2}}{4 π^{2}})}^{\frac{1}{3}} (∵ GM = {gR}^{2})$

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