Question 358: Gravitation

Question

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

Accepted Answer

The gravitational acceleration at a distance 'r' from the center of the Earth, where 'r' is greater than the radius of the Earth (R), is given by the formula:
$$g' = \frac{GM}{r^2}$$
Here,
$g'$ is the gravitational acceleration at distance 'r' from the center of the Earth,
$G$ is the universal gravitational constant,
$M$ is the mass of the Earth,
$r$ is the distance from the center of the Earth to the point where the gravitational acceleration is being calculated.
In this case, we're looking at a height 'R' above the Earth's surface, so the distance 'r' from the center of the Earth becomes $r = R + R = 2R$. Substituting this into our formula gives us:
$$g' = \frac{GM}{(2R)^2}$$
$$g' = \frac{GM}{4R^2}$$
Now, the acceleration due to gravity on the surface of the Earth (g) is given by:
$$g = \frac{GM}{R^2}$$
Comparing the two expressions, we can now express $g'$ in terms of $g$:
$$g' = \frac{g}{4}$$
Thus, the correct answer is Option C, which states that the gravitational acceleration at a height 'R' above the Earth's surface is $$\frac{g}{4}$$. This result demonstrates how gravitational acceleration decreases as one moves away from the surface of the Earth.

Answer

g

Answer

$$\frac{\mathrm{g}}{8}$$

Answer

$$\frac{g}{4}$$

Answer

$$\frac{g}{2}$$

Gravitation

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

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