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Acceleration Due to Gravity

Calculate the...

Question

Calculate the value of acceleration due to gravity at a point 5.0 km above earth's surface.

49 m / s^{2}

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$1.96 m / s^{2}$

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$8.76 m / s^{2}$

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$9.78 m / s^{2}$

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Solution

The correct option is D
$9.78 m / s^{2}$

The value of g at a height h is (h<<r)
$g = g_{0} (1 - \frac{2 h}{r})$
So, $g = 9.8 (1 - \frac{2 \times 5}{6400}) = 9.78 m / s^{2}$

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