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Physics

Mechanics

Easy

Question

$text A satellite of mass end text straight m text is in a circular orbit of radius end text 2 R subscript straight F text about the earth. The energy required end text text to transfer it to a circular orbit of radius end text 4 R subscript E text is (where end text M subscript E text and end text R subscript E text is the mass and radius of end text t h e space e a r t h space r e s p e c t i v e l y right parenthesis$

$\frac{G M_{E} m}{2 R_{E}}$
$\frac{G M_{E} m}{4 R_{E}}$
$\frac{G M_{E} m}{8 R_{E}}$
$\frac{G M_{E} m}{16 R_{E}}$

The correct answer is: $fraction numerator G M subscript E m over denominator 8 R subscript E end fraction$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell E subscript i equals negative fraction numerator G M subscript E m over denominator 4 R subscript E end fraction end cell row cell E subscript f equals negative fraction numerator G M subscript E m over denominator 8 R subscript E end fraction end cell row cell straight capital delta E equals E subscript f minus E subscript i end cell row cell straight capital delta E equals negative fraction numerator G M subscript E m over denominator 8 R subscript E end fraction minus open parentheses negative fraction numerator G M subscript E m over denominator 4 R subscript E end fraction close parentheses end cell row cell equals negative fraction numerator G M subscript E m over denominator 8 R subscript E end fraction plus fraction numerator G M subscript E m over denominator 4 R subscript E end fraction equals fraction numerator G M subscript E m over denominator 8 R subscript E end fraction end cell end table$

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