Mark the correct statements.

Options

A. Gravitational potential at the centre of curvature of a thin hemispherical shell of radius `R` and mass `M` is equal to `GM//R`.
B. Gravitational field strength at a point lying on the axis of a thin, uniform circular ring of radius R and mass M is equal to `GMx//[(R^(2)+x^(2))^(3/2)]` where `x` is distance of that point from the centre of the ring.
C. Newton's law of gravitation for gravitational force between two bodies is applicable only when bodies have spherical symmetric distribution of mass.
D. None of these

Explanation

To solve the question regarding the correctness of the statements about gravitational potential and gravitational field strength, we will analyze each statement step by step.

### Step 1: Analyze the first statement
The first statement claims that the gravitational potential at the center of the curvature of a thin hemispherical shell of radius \( R \) and mass \( M \) is equal to \( -\frac{GM}{R} \).

**Solution:**
The gravitational potential \( V \) at a distance \( r \) from a mass \( M \) is given by the formula:
\[ V = -\frac{GM}{r} \]
For a hemispherical shell, the potential at the center (which is at a distance \( R \) from the mass) would indeed be:
\[ V = -\frac{GM}{R} \]
Thus, the first statement is **correct**.

### Step 2: Analyze the second statement
The second statement discusses the gravitational field strength at a point lying on the axis of a thin uniform circular ring of radius \( R \) and mass \( M \).

**Solution:**
The gravitational field strength \( g \) at a point on the axis of a ring is given by:
\[ g = \frac{GMx}{(R^2 + x^2)^{3/2}} \]
where \( x \) is the distance from the center of the ring along the axis. The statement mentions this formula, which is indeed correct.

Thus, the second statement is **correct**.

### Step 3: Analyze the third statement
The third statement claims that Newton's law of gravitation is applicable only when bodies have a spherical symmetrical distribution of mass.

**Solution:**
Newton's law of gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law holds true for any distribution of mass, not just spherical distributions. Therefore, the third statement is **incorrect**.

### Summary of the Statements
1. **First Statement:** Correct
2. **Second Statement:** Correct
3. **Third Statement:** Incorrect

### Final Answer:
The correct statements are the first and second statements.

---