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Physics

Mechanics

Easy

Question

A body weighs 72N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

16 N
28 N
32 N
72 N

The correct answer is: 32 N

Weight of body on the surface of the earth $equals m space g equals 72 space N$
$table attributes columnalign left end attributes row cell g subscript h equals fraction numerator g R subscript E superscript 2 over denominator open parentheses R subscript E plus h close parentheses squared end fraction equals fraction numerator g R subscript E superscript 2 over denominator open parentheses R subscript E plus R subscript E over 2 close parentheses squared end fraction equals 4 over 9 g open parentheses therefore h equals R subscript E over 2 close parentheses end cell row cell F equals m g subscript h equals m cross times 4 over 9 g equals 4 over 9 cross times m g equals 4 over 9 cross times 72 N equals 32 N end cell end table$

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