JEE MAIN - Physics (2021 - 26th February Evening Shift - No. 27)
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 ________.
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Answer
4
Explanation
$${g_A} = {{GM(r)} \over {{R^3}}}$$
$${g_C} = {{GM} \over {{{\left( {R + {R \over 2}} \right)}^2}}}$$
Given, gA = gC
$$ \Rightarrow {{GM(r)} \over {{R^3}}} = {{GM} \over {{{\left( {R + {R \over 2}} \right)}^2}}}$$
$$ \Rightarrow {r \over {{R^3}}} = {4 \over {9{R^2}}}$$
$$ \Rightarrow r = {{4R} \over 9}$$
$$ \therefore $$ $$OA = {{4R} \over 9}$$
$$ \therefore $$ $$AB = R - r = {{5R} \over 9}$$
$$ \therefore $$ $$OA:AB = 4:5$$
$$ \therefore $$ x = 4
$${g_C} = {{GM} \over {{{\left( {R + {R \over 2}} \right)}^2}}}$$
Given, gA = gC
$$ \Rightarrow {{GM(r)} \over {{R^3}}} = {{GM} \over {{{\left( {R + {R \over 2}} \right)}^2}}}$$
$$ \Rightarrow {r \over {{R^3}}} = {4 \over {9{R^2}}}$$
$$ \Rightarrow r = {{4R} \over 9}$$
$$ \therefore $$ $$OA = {{4R} \over 9}$$
$$ \therefore $$ $$AB = R - r = {{5R} \over 9}$$
$$ \therefore $$ $$OA:AB = 4:5$$
$$ \therefore $$ x = 4
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