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Question: Answered & Verified by Expert
Choose the correct statement.
PhysicsGravitationTS EAMCETTS EAMCET 2020 (10 Sep Shift 1)
Options:
  • 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.
  • D Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.
Solution:
2468 Upvotes Verified Answer
The correct answer is: Acceleration due to gravity decreases with increasing depth assuming earth to be a sphere of uniform density.
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.

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