Acceleration due to gravity

Acceleration due to gravity
  1. increases with altitude
  2. decreases with altitude
  3. is independent of altitude
  4. first decreases and then increases with altitude

Solution

Acceleration due to gravity above the surface (at altitude) is given as \(\begin{aligned} & g^{\prime}=\frac{g}{\left(1+\frac{h}{R_e}\right)^2}=g\left(1+\frac{h}{R_e}\right)^{-2} \\ & g^{\prime}=g\left(1-\frac{2 h}{R_e}\right) \quad \ldots (i) \end{aligned}\) [By binomial theorem \((1+x)^n=1+n x\), when \(x < 1\)] From Eq. (i), it is clear that acceleration due to gravity decreases with altitude.

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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