Question

Find the percentage decrease in the weight of the body when taken to a height of 32km above the surface of the earth radius of earth is 6400km.

Answer 1

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Answer 2

Percentage decrease in weight of body is 1%.

Solution:

Given: Height = 32 km

           Radius of the earth = 6400 km.

The formula to find the gravitational pull at a height above surface of earth is given by $\bold{g=g_{0}\left(1-\frac{2 h}{R}\right)}$  

Rearranging the equation we get $\frac{2 h}{R}=g_{0}-g$  

Therefore percentage decrease $=\frac{2 h}{R} \times 100 \%$

On evaluating we get the percentage decrease in acceleration due to gravity is $2 \times \frac{32}{6400} \times 100 \%=1 \%$

As g is 1% less than $\bold{g_{0}}$, weight mg is also 1% less than $\bold{m g_{0}}$.