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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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