g inside and outside the earth
"g inside and outside the earth" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "g above and below the surface" in Gravitation. Slide it from the centre of the earth, out through the surface, to three earth radii away. Inside, only the orange sphere below the mass pulls; the grey shell above it pulls with zero net force. G(d) = g(1 − d/R_E) below the surface and g(h) = g R_E²/(R_E + h)² above it. g is largest on the surface and zero at the centre. JEE Main asked 39 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson g above and below the surface in Gravitation. Change the values and watch what happens.
In JEE Main
42 shifts analysed
39 questions from Gravitation across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §7.6
- At height h the distance from the centre is R_E + h, so g(h) = G M_E / (R_E + h)² = g (R_E/(R_E + h))².
- For h much smaller than R_E, the binomial approximation gives g(h) ≈ g (1 − 2h/R_E).
- At depth d, the shell of thickness d above pulls with zero net force; only the inner sphere of radius R_E − d, of mass M_E (R_E − d)³/R_E³, pulls.
- So g(d) = g (1 − d/R_E) exactly, for a uniform earth. At the centre (d = R_E) g is zero.
- g is greatest on the surface and falls whether you go up or down. For the same small distance, going up reduces g about twice as much as going down: 32 km up gives about 9.70 m/s², 32 km down about 9.75 m/s².
- Weight changes with g, mass does not. A body weighing 63 N on the surface weighs 63/(1.5)² = 28 N at a height R_E/2; one weighing 250 N weighs 125 N halfway to the centre.
- Use the exact form (R_E/(R_E + h))² whenever h is comparable to R_E; 1 − 2h/R_E gives nonsense there (zero at h = R_E/2).
Questions
3 answers
- What does the "g inside and outside the earth" simulation show?
- Slide it from the centre of the earth, out through the surface, to three earth radii away. Inside, only the orange sphere below the mass pulls; the grey shell above it pulls with zero net force.
- Does JEE Main ask questions from Gravitation?
- Yes. JEE Main asked 39 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "g above and below the surface" in Gravitation (Class 11 Physics).
Embed this simulation
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