QJEEM24Ph1753: JEE Main 2024 Physics - Class 11 JEEM24Ph1753 Solution: Assuming the earth to be a sphere of uniform mass density, a…

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:

$$F=F_0(1-\frac{d}{R})$$

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:

$$F=300(1-\frac{\frac{R}{4}}{R})$$

$$F=300(1-\frac{1}{4})$$

$$F=300\left(\frac{3}{4}\right)$$

$$F=225\text{N}$$

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.