JEE Main · 2021 · 26 Feb 2021 · Shift 2 · 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

O A : A B

will be

x : y

. The value of

x

is ____

Answer: 4

Solution

Above the surface, at the height

h = 3200

km of the point

C

g_{C} = \frac{GM}{( R + h ) ^{2}}

Below the surface, at a distance

O A

from the centre,

g_{A} = \frac{GM ( O A )}{R ^{3}}

Equating the two values with

R = 6400

km and

R + h = 9600

km,

O A = \frac{R ^{3}}{( R + h ) ^{2}} = \frac{( 6400 ) ^{3}}{( 9600 ) ^{2}} = \frac{25600}{9} km

Then

A B = R - O A = 6400 - \frac{25600}{9} = \frac{32000}{9}

km, so

O A : A B = 25600 : 32000 = 4 : 5

The ratio

O A : A B

4 : 5

, so

x = 4

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Integer answer

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