Question

The height at which the acceleration due to gravity decreases by 36% of its value on the surface of the earth.

Answer 1

Answer:

Explanation:

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Answer 2

To find:

Height at which acceleration of gravity decreases by 36% , assuming radius of Earth as R

Concept:

As per the question , the gravity decreases by 36% , so the new acceleration due to gravity will be 64% as that of gravity at surface.

Calculation:

Let new gravity be g" $\begin{lgathered}g" = \frac{64}{100} g \\\end{lgathered}$

$\begin{lgathered}= > \frac{g}{ {(1 + \frac{h}{R}) }^{2} } = \frac{64}{100} g \\\end{lgathered}$

$\begin{lgathered}= > {(1 + \frac{h}{R}) }^{2} = \frac{100}{64} \\\end{lgathered}$

$\begin{lgathered}= > 1 + \frac{h}{R} = \frac{10}{8} \\\end{lgathered}$

$\begin{lgathered}= > \frac{h}{R} = \frac{10}{8} - 1 \\\end{lgathered}$

$\begin{lgathered}= > \frac{h}{R} = \frac{2}{8} \\\end{lgathered}$

$\begin{lgathered}= > h = \frac{R}{4} \\\end{lgathered}$

【 So, height is ¼ of radius of Earth.】