This question contains Statement -1 and Stantement -2 Of the four choices given after the statements, choose the one that best desctibes the two statemesnts.
Statement -1:
For a mass M kept at the center of a cube of side 'a', the flux of gravitational field passing through its sides `4piGM.`
Statement -2:
If the direction of a field due to a point source is radial and its dependence on the distance 'r' from the source is given as `(1)/(r^2)`, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

Options

A. Option1 Statement-1 is false, Statement-2 is true
B. Option2 Statement-1 is true, Statement-2 is true, Statement -2 is correct explanation for Statement-1
C. Option3 Statement-1 is true, Statement-2 is true, Statement -2 is not a correct explanation for Statement-1
D. Option4 Statement-1 is true, Statement-2 is false

Answer

To solve the given problem, we will analyze both statements and apply the relevant concepts from gravitation and Gauss's law.

### Step-by-Step Solution:

**Step 1: Analyze Statement 1**
- Statement 1 claims that for a mass \( M \) located at the center of a cube with side length \( a \), the flux of the gravitational field passing through its sides is \( 4\pi GM \).
- To find the gravitational flux through the surface of the cube, we can use Gauss's law for gravitation, which states that the total gravitational flux \( \Phi \) through a closed surface is proportional to the enclosed mass \( M \):
\[ \Phi = -\frac{GM}{r^2} \cdot A \]
where \( A \) is the area of the surface.
- Since the mass is at the center of the cube, we can consider the total flux through the cube:
\[ \Phi = -4\pi GM \]
(the negative sign indicates the direction of the gravitational field is towards the mass).
- Therefore, Statement 1 is true.

**Step 2: Analyze Statement 2**
- Statement 2 states that if the direction of a field due to a point source is radial and its dependence on the distance \( r \) from the source is given as \( \frac{1}{r^2} \), then the flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.
- This is a direct application of Gauss's law, which applies to any field that follows the inverse square law (like gravitational and electrostatic fields).
- The flux through a closed surface surrounding a point source is given by:
\[ \Phi = -\frac{GM}{r^2} \cdot A \]
This shows that the flux depends only on the enclosed mass \( M \) and is independent of the surface's size or shape.
- Hence, Statement 2 is also true and correctly explains Statement 1.

**Conclusion:**
Both statements are true, and Statement 2 provides a correct explanation for Statement 1. Therefore, the correct option is that both statements are true and Statement 2 is the correct explanation of Statement 1.

### Final Answer:
Both statements are true, and Statement 2 is the correct explanation of Statement 1.

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