NEET 2025 Physics gravitational force MCQ Question

To solve the problem of determining the gravitational force experienced by a body at a height equal to one-third the radius of the Earth from its surface, we will utilize the concept of gravitational force and its dependence on distance from the center of the Earth.

Step 1: Understanding the Problem

The weight of the body on the surface of the Earth is given as $W = 48 \, \text{N}$. This weight is the gravitational force acting on the body at the surface, which can be expressed using the formula:

$$W = mg$$

where:

• $m$ is the mass of the body,
• $g$ is the acceleration due to gravity on the surface of the Earth, approximately $9.8 \, \text{m/s}^2$.

Step 2: Finding the Mass of the Body

From the weight, we can derive the mass of the body:

$$m = \frac{W}{g} = \frac{48 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 4.90 \, \text{kg}$$

Step 3: Gravitational Force at Height

We need to calculate the gravitational force at a height $h$ from the Earth's surface. The height $h$ is given as one-third the radius of the Earth, denoted by $R$:

$$h = \frac{1}{3}R$$

At this height, the distance from the center of the Earth becomes:

$$d = R + h = R + \frac{1}{3}R = \frac{4}{3}R$$

Step 4: Using the Gravitational Force Formula

The gravitational force $F$ at a distance $d$ from the center of the Earth is given by the formula:

$$F = \frac{GMm}{d^2}$$

Where:

• $G$ is the gravitational constant,
• $M$ is the mass of the Earth.

At the Earth's surface, the gravitational force is:

$$g = \frac{GM}{R^2}$$

Thus, we can relate the gravitational force at height $h$ to the gravitational force at the surface:

$$F = \frac{GMm}{\left(\frac{4}{3}R\right)^2} = \frac{GMm}{\frac{16}{9}R^2} = \frac{9}{16} \cdot \frac{GMm}{R^2} = \frac{9}{16}mg$$

Step 5: Calculating the Gravitational Force

Now substituting $mg = 48 \, \text{N}$:

$$F = \frac{9}{16} \cdot 48 \, \text{N}$$

Calculating this gives:

$$F = \frac{9 \times 48}{16} = \frac{432}{16} = 27 \, \text{N}$$

Conclusion

Thus, the gravitational force experienced by the body at a height of one-third the radius of the Earth from its surface is $27 \, \text{N}$. Therefore, the correct answer is:

B) 27 N.

Clarification of Other Options

1. Option A (16 N): This value is too low; it does not take into account the proper scaling of gravitational force with distance.
2. Option C (32 N): This value incorrectly assumes a different ratio of gravitational force reduction.
3. Option D (36 N): Similarly, this does not match the calculated gravitational reduction at the specified height.

In summary, the correct understanding of gravitational force variation with height led us to the correct answer of $27 \, \text{N}$.