Question 80: Gravitation

Question

Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \mathrm{~N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

Accepted Answer

To solve this question, we first need to understand how gravitational force (and hence weight) changes with depth under the surface of the Earth. The gravitational force at a depth $d$ is given by the formula:
$$ F = F_0 \left(1 - \frac{d}{R}ight) $$
where $F_0$ is the gravitational force (or the weight) at the surface, $R$ is the radius of the Earth, and $d$ is the depth below the Earth's surface.
In your question, the body weighs 300 N on the surface, so $F_0 = 300$ N. It is taken to a depth of $\frac{R}{4}$ under the surface. Therefore, $d = \frac{R}{4}$.
Substituting these values into our formula, we get:
$$ F = 300 \left(1 - \frac{\frac{R}{4}}{R}ight) $$
$$ F = 300 \left(1 - \frac{1}{4}ight) $$
$$ F = 300 \left(\frac{3}{4}ight) $$
$$ F = 225 \, 	ext{N} $$
Therefore, at a depth of $\frac{R}{4}$ under the surface of the Earth, the body would weigh 225 N. The correct option is
Option D
.

Answer

75 N

Answer

375 N

Answer

300 N

Answer

225 N

Gravitation

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

Choose the correct answer: