Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
If a satellite orbits as close to the earth's surface as possible: (1) its time period of rotation is minimum (2) its speed is maximum (3) the total energy of the earth plus satellite system is minimum (4) the total energy of the earth plus satellite system is maximumA) 1 and 2 are correct
B) 2 and 3 are correct
C) 1 and 4 are correct
D) 1, 2 and 3 are correct
Correct Answer: D
Solution :
Orbital speed of satellite \[{{v}_{o}}=\sqrt{\frac{GM}{R+h}}\] When satellite is orbiting close to earth, then\[h\to 0\], so, \[{{v}_{o}}=\sqrt{\frac{GM}{R}}=maximum\] Time period of satellite, \[T=\frac{2\pi (R+h)}{{{v}_{o}}}is\text{ }minimum\] Total energy\[=\frac{1}{2}mv_{o}^{2}-\frac{GMm}{R}\] \[=\frac{1}{2}m\frac{GM}{R}-\frac{GMm}{R}\] \[=-\frac{1}{2}\frac{GMm}{R}=\min imum\]
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