If g is the acceleration due to gravity on the surface of the Earth, what is its value at a depth equal to half the radius of the Earth?

1. If g is the acceleration due to gravity on the surface of the Earth, what is its value at a depth equal to half the radius of the Earth?

A) \( g/4 \)
B) \( g/2 \)
C) \( g/3 \)
D) \( g/9 \)

... Answer is B)

To find the acceleration due to gravity at a depth \( d \), we use the formula:

\( g_d = g \left( 1 - \frac{d}{R} \right) \)

Here, \( d = \frac{R}{2} \). Substituting into the formula:

\( g_d = g \left( 1 - \frac{\frac{R}{2}}{R} \right) \)

Simplify the terms:

\( g_d = g \left( 1 - \frac{1}{2} \right) \)

\( g_d = g \cdot \frac{1}{2} \)

Thus, the acceleration due to gravity at a depth equal to half the Earth's radius is:

\( g_d = \frac{g}{2} \)

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