IF `eta` denotes coefficient of viscosity and G denotes gravitational constant then, `Gxxeta` yields the dimensions

Options

A. `[M^(2)L^(0)T^(-3)]`
B. `[MLT^(-3)]`
C. `[ML^(2)T^(-2)]`
D. `[M^(0)L^(2)T^(-3)]`

Explanation

To find the dimensions of the product of the gravitational constant \( G \) and the coefficient of viscosity \( \eta \), we will follow these steps:

### Step 1: Identify the dimensions of \( G \) and \( \eta \)

1. **Gravitational Constant \( G \)**:
- The dimension of \( G \) is given as:
\[ [G] = M^{-1} L^3 T^{-2} \]

2. **Coefficient of Viscosity \( \eta \)**:
- The dimension of \( \eta \) is given as:
\[ [\eta] = M L^{-1} T^{-1} \]

### Step 2: Multiply the dimensions of \( G \) and \( \eta \)

Now, we will find the dimensions of the product \( G \cdot \eta \):
\[ [G \cdot \eta] = [G] \cdot [\eta] = (M^{-1} L^3 T^{-2}) \cdot (M L^{-1} T^{-1}) \]

### Step 3: Combine the dimensions

Now we will combine the dimensions by adding the powers of the same base:
- For mass \( M \):
\[ M^{-1} \cdot M = M^{(-1 + 1)} = M^0 \]
- For length \( L \):
\[ L^3 \cdot L^{-1} = L^{(3 - 1)} = L^2 \]
- For time \( T \):
\[ T^{-2} \cdot T^{-1} = T^{(-2 - 1)} = T^{-3} \]

### Step 4: Write the final dimensions

Combining all these results, we have:
\[ [G \cdot \eta] = M^0 L^2 T^{-3} \]

### Conclusion

The dimensions of the product \( G \cdot \eta \) are:
\[ M^0 L^2 T^{-3} \]