Question

If g = 9.8 m/s? on the surface if the earth, find the acceleration due to gravity if h = R/2 from the
surface of the earth.
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Answer 1

Question :-

If g = 9.8 m/s² on the surface of the earth. Find the acceleration due to gravity at height h if h = R/2 from the surface of the earth.

Answer :-

Given :-

• g = 9.8 m/s²
• h = R/2

To Find :-

• Acceleration due to gravity

Solution :-

Acceleration due to gravity at height h :-

$\sf g' = g \times \dfrac{1}{\Big(1 + \dfrac{h}{R}\Big)^{2} }$

Substituting the values :-

$\implies\sf g' = 9.8 \times \dfrac{1}{\Big(1 + \dfrac{\frac{\cancel R}{2}}{\cancel{R}}\Big)^{2} }$

$\implies\sf g' = 9.8 \times \dfrac{1}{\Big(1+\dfrac{1}{2}\Big)^2}$

$\implies\sf g' = 9.8 \times \dfrac{1}{\Big(\dfrac{3}{2}\Big)^2}$

$\implies\sf g' = 9.8 \times \dfrac{1}{\frac{9}{4}}$

$\implies\sf g' = 9.8 \times \dfrac{4}{9}$

$\implies\sf g' = 4.35$

Acceleration due to gravity at height h if h = R/2 from the surface of the earth is 4.35 m/s².