JEE Main 2020 · 5 September · morning · Single correct · +4 / −1

The value of the acceleration due to gravity is g₁ at a height h = R/2 (R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio ( d/R ) equals :

  1. (a) 5/9
  2. (b) 1/9
  3. (c) 7/9
  4. (d) 4/9
Answer and solution

Answer (a) 5/9

Solution

Physics sir · 3 steps

Find g₁ at height R/2 first, then ask how deep you must dig to get the same fraction of g.

  1. At the height. Above the surface, gₕ = g/(1 + h/R)². The height h = R/2 is large, so the approximation g(1 - 2h/R) does not work here. Use the exact formula.

    g₁ = g/(1 + 1/2)² = g/(9/4) = 4/9 g

  2. At the depth. Below the surface, g_d = g(1 - d/R). Set this equal to g₁: 1 - d/R = 4/9.
  3. So. d/R = 1 - 4/9 = 5/9, which is option (a).

The idea to keep. Above the surface g falls as 1/r². Inside the earth it falls linearly with depth. Use the exact height formula whenever h is not small compared with R.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 160 times in JEE Main since 2020. This question is from 2020.