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There is a mine of depth about 3.0 km. Conditions prevailing in this mine as compared to those at the surface of earth are

  • A.higher air pressure, lower acceleration due to gravity
  • B.higher air pressure, higher acceleration due to gravity
  • C.lower air pressure, higher acceleration due to gravity
  • D.lower air pressure, lower acceleration due to gravity
  • E.same air pressure and acceleration due to gravity

Answer: A

The mine has higher air pressure, lower acceleration due to gravity.

Air pressure increases as you go down, because there is a taller column of air above. Gravity decreases with depth: \(g_{d} = g\left(1 - \frac{d}{R}\right)\), since only the mass of the earth beneath you attracts you as if from the centre.

The change in \(g\) at 3 km is small (about 0.05%), but its direction is downward, which rules out the options with higher \(g\). Lower pressure would apply to a mountain top, not a mine.

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