Question

For physics experts
An artificial satellite is moving in a circular orbit around the earth with a speed equal to the escape velocity from the radius of Earth R. Then what is the height of the satellite above the surface of the earth??

a ) R/2
b ) R
c ) 3R
d ) none

• Give proper explanation
• Spam will be deleted
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Answer 1

Answer:

( b ) R is the right answer

Answer 2

Answer:

b ) R

Explanation:

Orbital radius of a satellite = r = h + R

$\sf \: V = \sqrt{ \frac{GM}{R} } = \sqrt{ \frac{GM}{R + h} } (M = mass \: of \: the \: earth)$

$\sf \: Ve = \sqrt{ \frac{2GM }{R } } \Rightarrow v= \frac{ve}{2} \\ \sf \: \sqrt{ \frac{GM}{R} } + \frac{1}{2} = \sqrt{ \frac{2GM}{R} } \Rightarrow \: squaring \: both \: sides \\ \sf \: { \dfrac { \cancel{GM}}{R} } = \frac{1}{4} = \frac{2 \cancel{GM}}{R} \Rightarrow \frac{1}{R+h} = \frac{1}{2R} \\ \sf \: 2R=R+h \Rightarrow h =2R-R= \underline \red{{ R}}$

${\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{{hope \: it \: helps \: }} ⇢}}}}}}$