Question

The acceleration due to gravity would be half its value at sea level at an altitude
A)R B)2^2R C)(2^2-1)R D)(2^2+1)R

Answer 1

Answer:

The acceleration due to gravity would be half its value at sea level at an altitude $h = (\sqrt2 - 1)R$

Explanation:

As we know that the acceleration due to gravity is given as

$a = \frac{GM}{r^2}$

at sea level the acceleration due to gravity is known as

$g = \frac{GM}{R^2}$

now at some altitude above this the acceleration due to gravity will be half of its value at sea level

so we will have

$\frac{1}{2}\frac{GM}{R^2} = \frac{GM}{(R + h)^2}$

now we have

$(R + h)^2 = 2 R^2$

$R + h = \sqrt2 R$

$h = (\sqrt2 - 1)R$

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Topic : acceleration due to gravity

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