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Gravitation question

2017 · Q153
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Gravitation question

2017 · Q153

NEETPhysicsGravitationMCQ+4 / −1
The acceleration due to gravity at a height at a height 1 km above the rearth is the same as at a depth d below the surface of earth. Then
  1. A
    d = 1 km
  2. B
    d = 32{3 \over 2}23​ km
  3. C
    d = 2 km
  4. D
    d = 12{1 \over 2}21​ km
View written solutionFree

Correct answer: C

Above earth surface

gh=g(1−2hRe){g_h} = g\left( {1 - {{2h} \over {{R_e}}}} \right)gh​=g(1−Re​2h​)

Below earth surface

gd=g(1−dRe){g_d} = g\left( {1 - {d \over {{R_e}}}} \right)gd​=g(1−Re​d​)

According to question, gh = gd

g(1−2hRe)g\left( {1 - {{2h} \over {{R_e}}}} \right)g(1−Re​2h​) = g(1−dRe)g\left( {1 - {d \over {{R_e}}}} \right)g(1−Re​d​)

Clearly, d = 2h = 2 km

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