The acceleration due to gravity at a depth equal to R/2 from the Earth’s surface is _________. (Let acceleration due to gravity on the Earth’s surface be $g_{0}$ )

$\frac{4 g_{0}}{10}$

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$\frac{g_{0}}{4}$

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$2 g_{0}$

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$\frac{g_{0}}{2}$

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Solution

The correct option is D
$\frac{g_{0}}{2}$

Step 1: Given data
Depth = $\frac{R}{2}$ , (where $R$ is the radius of the earth)
acceleration due to gravity at the surface of the earth $= g_{0}$
Step 2: formula used;
Acceleration due to the gravity at some depth is given as $g_{d} = g_{0} (1 - \frac{d}{R})$
(where $d = d e p t h$ )
Step 3: calculate the value of $g_{d}$
According to the question, the depth is $\frac{R}{2}$
Now, substitute the values in the above equation,
$g_{d} = g_{0} (1 - \frac{\frac{R}{2}}{R}) = \frac{g_{0}}{2}$
Therefore the new acceleration due to gravity is half of the original acceleration due to gravity.
Hence, the correct option is (D) $\frac{g_{0}}{2}$

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The acceleration due to gravity at a depth equal to R/2 from the Earth’s surface is _________. (Let acceleration due to gravity on the Earth’s surface be g0)

The acceleration due to gravity at a depth equal to R/2 from the Earth’s surface is _________. (Let acceleration due to gravity on the Earth’s surface be $g_{0}$ )