First slide

Acceleration due to gravity and its variation

Question

Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth

Easy

A
B
C
D

None of these

Solution

$a c c e l e r a t i o n d u e t o g r a v i t y i n s i d e t h e e a r t h, g = \frac{G M}{R^{3}} r i . e ., g \propto r (if r < R) a c c e l e r a t i o n d u e t o g r a v i t y o n t h e e a r t h, g = \frac{G M}{R^{2}} a n d a c c e l e r a t i o n d u e t o g r a v i t y a t a d i s \tan c e r (r > R) f r o m s u r f a c e o f t h e e a r t h, g = \frac{G M}{r^{2}} \Rightarrow g \propto \frac{1}{r^{2}} (i f r > R)$

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