Question 269: Gravitation

Question

A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

Accepted Answer

When calculating the gravitational force on a body at a height above Earth's surface, we use the formula for acceleration due to gravity at a height $ h $ equal to half the radius of Earth, $ \left(h=\frac{R}{2}ight) $. The modified acceleration due to gravity, $ g_h $, is expressed as:
$ g_h = \left( \frac{n}{n+1} ight)^2 g $
Here, $ n = 2 $, because the height is half the Earth's radius. Substituting the value of $ n $:
$ g_h = \left( \frac{2}{2+1} ight)^2 g = \left( \frac{2}{3} ight)^2 g = \frac{4}{9} g $
The weight of the boy at this height, $ W_h $, is calculated by multiplying his weight at Earth's surface by this modified gravitational acceleration:
$ W_h = m \cdot g_h = \frac{4}{9} 	imes mg $
Given that $ mg = 72 \, 	ext{N} $, we substitute this into the equation:
$ W_h = \frac{4}{9} 	imes 72 = 32 \, 	ext{N} $
Thus, the gravitational force on the boy at this height is 32 N.

Answer

32 N

Answer

48 N

Answer

96 N

Answer

162 N

Gravitation

A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

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