In reported figure of earth, value of acceleration due to gravity is same at point A and C but it is

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7.Gravitation

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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 $\ldots \ldots \ldots$

A

$3$

B

$5$

C

$4$

D

$6$

(JEE MAIN-2021)

Solution

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

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

$g_{A}=g_{C}$

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

so $OA =\frac{4 R }{9} ; AB = R – r =\frac{5 R }{9}$

$OA : AB =4: 5$

Standard 11

Physics

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