A) h : 2R
B) 2h : R
C) R : h
D) h : R
Correct Answer: B
Solution :
The work obtained in bringing a body from infinity to a point in a gravitational Held is called the gravitational potential energy of the body at that point. \[U=\int_{R}^{R+h}{\frac{GMm}{{{r}^{2}}}}dr\] The energy required to raise the satellite is \[U=-GMm\left[ \frac{1}{R+h}-\frac{1}{R} \right]\] \[U=\frac{mgRh}{R+h}\] ?(i) The orbital velocity of a satellite is given by \[{{v}_{o}}=\sqrt{\frac{g{{R}^{2}}}{R+h}}\] Kinetic energy \[KE=\frac{1}{2}mv_{o}^{2}\] \[KE=\frac{1}{2}m\frac{g{{R}^{2}}}{R+h}\] ?(ii) Dividing Eq., (i) by (ii), we get \[\frac{U}{KE}=\frac{mgRh}{(R+h)\times \frac{1}{2}m\times \frac{g{{R}^{2}}}{R+h}}=\frac{2h}{R}\] \[\therefore \] \[\frac{U}{KE}=\frac{2h}{R}\]
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