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EEJ MAIN Physics QUESTION #7001
Question 1

The graph best representing the variation of acceleration due to gravity $g$ with distance $d$ from Earth's centre (Earth's radius $= R$) shows which behaviour?

  • $g$ peaks sharply at $d = R$ with linear rise inside and $1/d^2$ fall outside
  • $g$ increases exponentially throughout with no peak
  • $g$ rises linearly from 0 to a peak at $d = R$ then falls as $1/d^2$ outside✔️
  • $g$ is constant inside and decreases outside
Correct Answer Explanation

The correct behaviour of $g$:

  • Inside the Earth ($d < R$): $g = \frac{GM}{R^3}d$ — linear increase from $g=0$ at centre to $g_{surface}$ at $d=R$.
  • Outside the Earth ($d > R$): $g = \frac{GM}{d^2}$ — decreases as $1/d^2$.

The graph shows a straight line from origin to $(R, g_{max})$, then a smooth $1/d^2$ curve decreasing afterward. This is a linear rise inside and inverse-square fall outside, meeting at a sharp peak at $d = R$.