A body of weight W newton is at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

Options

(a) W/2
(b) 2W/3
(c) 4W/9
(d) 8W/27

Correct Answer:

4W/9

Explanation:

Let h=height above the earth
R=Radius of earth
Now, the acceleration due to gravity at a height ‘h’ above the earth’s surface(g) is given by
gh=g(1+h/R)⁻²
Given h=R/2
gh=g(1+R/2/R)⁻²
gh/g=1/(1+1/2)²=1/(3/2)²=(2/3)²=4/9
since g=W; gh=4/9g;4/9 W.

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