First slide

Variation of g

Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the size of the earth. If acceleration due to gravity on the surface of the earth is g and that on the surface of the new planet is g', then

Easy

A

g'= g / a
B

g' =27 g
C

g'= 9 g
D

g' = 3g

Solution

We know that,
$g = \frac{GM}{R^{2}} = \frac{G (\frac{4}{3} {πR}^{3}) ρ}{R^{2}}$
or $g = \frac{4}{3} πGRρ or g \propto R$
$\begin{array}{l} ∴ \frac{g^{'}}{g} = \frac{R^{'}}{R} = \frac{3 R}{R} = 3 \\ g^{'} = 3 g \end{array}$

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