Q134 / 160 · TS EAMCET 2020 (10 Sep Shift 1) · Physics

Choose the correct statement.

  • A
    Acceleration due to gravity increases with increasing altitude.
  • B
    Acceleration due to gravity is independent of mass of earth.
  • C
    A geostationary satellite can have a time period less than 24 h.
  • Correct answer
    D
    Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.

Solution

Acceleration due to gravity at altitude $h$ is $g_h=\frac{G M}{(R+h)^2}$ $\therefore g_h$ decreases with altitude. $g=\frac{G M}{R^2}, g \propto M$ Geostationary satellite has a time period of $24 \mathrm{~h}$. $g$ at depth $d$ is $g_d=g\left(\frac{R-d}{R}\right)$ $\therefore g$ decreases with increasing depth.

Hence, the correct answer is option: 'D'.

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