Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, \frac{T_{A}}{T_{B}} , is : 

Answers (1)

Orbital velocity of satellite -

V=\sqrt{\frac{GM}{r}}

r=R+h

r\rightarrow Position of satellite from the centre of earth

V\rightarrow Orbital velocity

- wherein

The velocity required to put the satellite into its orbit around the earth.

        A                            B

        m                           2m

        R                            2R

       T_{A}                         T_{B}

T = kinetic energy 

So, V_{o} = Orbital Velocity =\sqrt{\frac{GM_{c}}{r}}=V

T=\frac{1}{2}mV_{o}^{2}=\frac{1}{2}mV^{2}

T_{A}=\frac{1}{2}m_{A}V_{A}^{2}

T_{B}=\frac{1}{2}m_{B}V_{B}^{2}

\frac{T_{A}}{T_{B}}=\frac{m_{A}}{m_{B}}\times (\frac{V_{A}}{V_{B}})^{2}=\frac{m}{2m}\times (\frac{\frac{GM_{c}}{R}}{\frac{GM_{c}}{2R}})=1

\frac{T_{A}}{T_{B}}=1

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