Which of the following are correct?

Options

A. Out of electrostatic, electromagnetic, nuclear and gravitational interactions, the gravitational interaction is the weakest.
B. If the earth were to 'rotate faster than its present speed, the weight of an object would decrease at the equator but remain unchanged at the poles.
C. The mass of the earth in terms of `g, R` and `G` is `(gR^(2)//G)`.
D. If the earth stops rotating in its orbit around the Sun there will be no variation in the weight of a body on the surface of earth.

Explanation

To determine which of the given statements are correct, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Statement:** Out of electrostatic, electromagnetic, nuclear, and gravitational interactions, gravitational interaction is weakest.

**Analysis:**
- Gravitational force is indeed the weakest of all the fundamental forces in nature.
- The hierarchy of forces from strongest to weakest is: nuclear > electromagnetic > electrostatic > gravitational.

**Conclusion:** Option 1 is **True**.

### Step 2: Analyze Option 2
**Statement:** If the Earth were to rotate faster than its present speed, the weight of an object would decrease at the equator but remain unchanged at the poles.

**Analysis:**
- As the Earth rotates, centrifugal force acts outward, which counteracts the gravitational force.
- At the equator, this centrifugal force is maximum due to the highest linear velocity.
- If the Earth rotates faster, the centrifugal force increases, leading to a decrease in the effective weight of objects at the equator.
- At the poles, the centrifugal force is zero since they lie on the axis of rotation, thus the weight remains unchanged.

**Conclusion:** Option 2 is **True**.

### Step 3: Analyze Option 3
**Statement:** In terms of the mass of Earth, g, r, and G, the relationship is given by g = (G * M) / r².

**Analysis:**
- The formula for gravitational acceleration (g) is derived from Newton's law of gravitation:
\[ g = \frac{G \cdot M}{r^2} \]
- Rearranging this gives us:
\[ M = \frac{g \cdot r^2}{G} \]
- The statement in the option is consistent with this equation.

**Conclusion:** Option 3 is **True**.

### Step 4: Analyze Option 4
**Statement:** If the Earth stops rotating in its orbit around the sun, there will be no variation in the weight of a body on the surface of the Earth.

**Analysis:**
- The weight of a body on the surface of the Earth is primarily determined by the gravitational force exerted by the Earth.
- The Earth's motion around the sun does not affect the gravitational force acting on objects on its surface.
- Therefore, even if the Earth were to stop its orbit around the sun, the weight of objects on its surface would remain unchanged.

**Conclusion:** Option 4 is **True**.

### Final Conclusion
All four options are correct.

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