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HEIGHT AT WHICH MAGNITUDE OF g WILL BE EQUAL TO THAT AT A DEPTH R/2 IS WHAT [ R= radius of earth ]

HEIGHT AT WHICH MAGNITUDE OF g WILL BE EQUAL TO THAT AT A DEPTH R/2 IS WHAT [ R= radius of earth ]

Grade:12

1 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Value of g at depth\dfrac{R}{2}=g(1-\dfrac{R/2}{R})=\dfrac{g}{2}

Let the height at which the magnitude of g is same beh.

Hence\dfrac{gR^2}{(R+h)^2}=\dfrac{g}{2}
\implies R+h=\sqrt{2}R
\implies h=(\sqrt{2}-1)R

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