In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)

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Verified Solution

Answer & Solution

Correct Answer

(C) \(4\)

Detailed explanation

\(g_{A}=\frac{G M(r)}{R^{3}}\)

\(g_{c}=\frac{G M}{\left(R+\frac{R}{2}\right)^{2}}\)

\(g_{A}=g_{C}\)

\(\frac{ r }{ R ^{3}}=\frac{1}{\frac{9}{4} R ^{2}} \Rightarrow r =\frac{4 R }{9}\)

so \(OA =\frac{4 R }{9} ; AB = R - r =\frac{5 R }{9}\)

\(OA : AB =4: 5\)

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