Q176 / 180 · KCET 2024 · Physics

What is the value of acceleration due to gravity at a height equal to half the radius of the Earth, from its surface?

Correct answer
A
$4.4 \mathrm{~ms}^{-2}$
B
$6.5 \mathrm{~ms}^{-2}$
C
Zero
D
$9.8 \mathrm{~ms}^{-2}$

Solution

Acceleration due to gravity at height $h$ from the surface of the earth. $g_h=\frac{g}{\left(1+\frac{h}{R}\right)^2}$ Given, $\quad h=\frac{R}{2}$ $\therefore \quad g_h=\frac{g}{\left(1+\frac{R}{R}\right)^2}=\frac{g}{\left(\frac{3}{2}\right)^2}$ $=\frac{4}{9} g=\frac{4}{9} \times 9.8=4.4 \mathrm{~m} / \mathrm{s}^2$

Hence, the correct answer is option: 'A'.

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