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Physics

Mechanics

Easy

Question

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

$(3 / 2) v$
$\sqrt{(3 / 2)} v$
$\sqrt{(2 / 3)} v$
$(2 / 3) v$

The correct answer is: $square root of left parenthesis 2 divided by 3 right parenthesis end root v$

$fraction numerator m v squared over denominator R end fraction equals fraction numerator G M m over denominator R squared end fraction text and end text fraction numerator m v squared over denominator R end fraction equals fraction numerator G M m over denominator R squared end fraction D i v i d i n g space left parenthesis i right parenthesis space b y space left parenthesis i i right parenthesis table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell v squared over v squared equals R over R v squared over v squared equals R to the power of apostrophe over R v to the power of apostrophe over v end cell row cell equals square root of R over R end root text as end text R equals fraction numerator 3 R over denominator 2 end fraction end cell row cell equals square root of 2 over 3 end root not stretchy rightwards double arrow v to the power of straight prime equals square root of 2 over 3 end root times v end cell end table$

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