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Physics

Mechanics

Easy

Question

A planet has mass 1/10 of that of earth, while radius is 1/3 that of earth. If a person can throw a stone on earth surface to a height of 90 m, then he will be able to throw the stone on that planet to a height

90 m
40 m
100 m
45 m

The correct answer is: 100 m

Acceleration due to gravity $g equals fraction numerator G M over denominator R squared end fraction$
$therefore g subscript text plapet end text end subscript over g subscript text earth end text end subscript equals M subscript text planet end text end subscript over M subscript text earth end text end subscript open parentheses R subscript text earts end text end subscript over R subscript text planet end text end subscript close parentheses squared equals 1 over 10 cross times open parentheses 3 over 1 close parentheses squared equals 9 over 10 H equals fraction numerator u squared over denominator 2 g end fraction rightwards double arrow H subscript text planat end text end subscript over H subscript text earth end text end subscript equals g subscript text earth end text end subscript over g subscript text planet end text end subscript rightwards double arrow H subscript text planet end text end subscript equals 10 over 9 cross times H subscript text earth end text end subscript equals 10 over 9 cross times 90 equals 100 space m e t r e$

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