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Question

In the reported figure of the earth, the value of acceleration due to gravity is the same at points 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:5. The value of x is ____________.


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Solution

Step 1: Given data

The value of acceleration due to gravity is the same at points A and C but it is smaller than that of its value at point B (surface of the earth).

And, OA:AB=x:5

Step 2: Let, Eg= The gravitational field of the earth and Rthe radius of the earth.

For inside point A,

Eg=GMr,R3where,r=OA Here G is gravitational constant

For outside point C,

Eg=GM,r2where,r=OC=R+R2=3R2

Step 3: Acceleration due to gravity is the same at both points, and so will the gravitational field.

GMrR3=GM3R22r=OA=4R9AB=OBOAAB=R4R9AB=5R9

Now,

OA:AB=4R9:5R9OA:AB=4:5=X:5X=4

Hence, the distance between the Earth's surface and its center is greater at the equator than at the poles, and the acceleration due to gravity is lowest there.


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