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Physics · JEE | GRAVITATION

हिन्दी

How is the acceleration due to gravity at a height \( h \) above the earth's surface approximated for \( h \ll R_E \)?

  1. A
    \( g(h) \approx g(1 - \frac{h}{R_E}) \)
  2. B
    \( g(h) \approx g(1 - \frac{2h}{R_E}) \)
  3. C
    \( g(h) \approx g(1 + \frac{2h}{R_E}) \)
  4. D
    \( g(h) \approx g(1 + \frac{h}{R_E}) \)
View Answer & Solution

Correct answer · Option B

\( g(h) \approx g(1 - \frac{2h}{R_E}) \)

Explanation

Using binomial expansion for \( h \ll R_E \), \( g(h) = \frac{GM_E}{R_E^2(1 + h/R_E)^2} \approx g(1 - \frac{2h}{R_E}) \).
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