Choose the correct alternative
(a)Acceleration due to gravity increase/decrease with increasing altitude.
(b) Acceleration due to gravity increase/decrease with increasing depth (assume the earth to be a sphere of uniform density).
(c ) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula `- GM m ((1)/(r_(2)) - (1)/(r_(1)))` is more/less accurate than the formula `mg (r_(2) - r_(1))` for the difference of potential energy between two points `r_(2)` and `r_(1)` distance away from the centre of earth.

Options

A. Acceleration due to gravity increases/decreases with increasing altitude.
B. Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density.)
C. Acceleration due to gravity is independent of the mass of the earth/mass of the body.
D. The formula – GMm `(1/r_2-1/r_1)` is more/less accurate than the formula mg `(r_2 – r_1)` for the difference of potential energy between two points `r_2` and `r_1` distance away from the centre of the earth.

Explanation

To solve the question, we will analyze each part step by step.

### Step 1: Acceleration due to gravity with increasing altitude
- The acceleration due to gravity \( g \) at a height \( h \) above the Earth's surface can be expressed as:
\[ g' = g \left(1 - \frac{2h}{R}\right) \]
where \( R \) is the radius of the Earth.
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