The height at which the weight of a body becomes 1/16 th, its weight

The height at which the weight of a body becomes 1/16 th, its weight on the surface of earth (radius R), is

(a) 5 R
(b) 15 R
(c) 3 R
(d) 4 R

3 R

Let at h height, the weight of a body becomes 1/16th of its weight on the surface.

Wh = 16 Ws g’ = GM/(Re+h)²

Similarly, g = GM/Re²

Now, g’/g = Re²/(Re+h)²

⇒ g’=g(1+h/R)⁻²

⇒ Wh = 16 Ws

⇒ g’ = g/16 g’

= 16g(1+h/R)⁻² 1/16

= (1+h/R)⁻²

⇒ 4 = 1+h/R

⇒ h = 3 R

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