Q128 / 180 · KCET 2016 · Physics
Variation of acceleration due to gravity \( (g) \) with distance \( x \) from the centre of the earth is best
represented by ( \( R \rightarrow \) Radius of the earth)
represented by ( \( R \rightarrow \) Radius of the earth)
- A

- B

- C

- Correct answerD

Solution
The acceleration due to gravity \( \mathrm{g} \) is proportional to \( \mathrm{r} \) till thesurface of Earth and is inversely proportional to \( r^{2} \) outside the
surface of Earth.
That is, \( g \propto r \); till surface of Earth
\( g \propto \frac{1}{r^{2}} \); outside the surface of Earth
Therefore, the graph shows linear behaviour till the surface of Earth, that is, till \( r \) and beyond \( R \) it shows \( \frac{1}{r^{2}} \) decay thus
the variation of \( g \) on the Earth is represented as

surface of Earth.
That is, \( g \propto r \); till surface of Earth
\( g \propto \frac{1}{r^{2}} \); outside the surface of Earth
Therefore, the graph shows linear behaviour till the surface of Earth, that is, till \( r \) and beyond \( R \) it shows \( \frac{1}{r^{2}} \) decay thus
the variation of \( g \) on the Earth is represented as

Hence, the correct answer is option: 'D'.