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MCQ practice · SSC Physics Board questions · Chapter 3: Force

Dinajpur Board 2023

The acceleration due to gravity at a height equal to the radius of the earth:

  1. i. is one quarter of the earth's acceleration due to gravity
  2. ii. is inversely proportional to the square of the earth's radius
  3. iii. depends on the height

Think it through first, then pick an option.

  1. a i and ii
  2. b i and iii
  3. c ii and iii
  4. d i, ii and iii
Answer and explanation

Correct answer: d i, ii and iii

For r = R, g′ = GM/(2R)² = g/4 (i), inversely proportional to R² (ii) and dependent on height (iii); all three are true.

Why the other options are wrong

  • a i and ii: iii is true as well: g′ depends on the height; i and ii alone leaves it out.
  • b i and iii: ii is true: g′ = GM/(R + R)² = GM/4R², inversely proportional to R²; so ii cannot be dropped.
  • c ii and iii: i is true: putting r = R in g′ = g/(1 + r/R)² gives g/4; so i cannot be dropped.