The intensity of solar radiation on the ẻarth is `450W/ (m)^(2)`. Assuming the earth to be perfect black body, if the radiation pressure on the earth is `pxx10^(-7) N/ m^2` then find `p`.

Answer

To solve the problem, we need to find the value of \( p \) given the intensity of solar radiation and the formula for radiation pressure. Here's the step-by-step solution:

### Step 1: Understand the given data
- The intensity of solar radiation \( I = 450 \, \text{W/m}^2 \)
- The speed of light \( c = 3 \times 10^8 \, \text{m/s} \)
- The radiation pressure \( p \times 10^{-7} \, \text{N/m}^2 \)

### Step 2: Use the formula for radiation pressure
The formula for radiation pressure \( P \) for a perfect black body is given by:
\[ P = \frac{I}{c} \]
where \( I \) is the intensity and \( c \) is the speed of light.

### Step 3: Substitute the values into the formula
Substituting the values of \( I \) and \( c \):
\[ P = \frac{450 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} \]

### Step 4: Calculate the radiation pressure
Calculating the above expression:
\[ P = \frac{450}{3 \times 10^8} = \frac{450}{300000000} = 1.5 \times 10^{-6} \, \text{N/m}^2 \]

### Step 5: Relate the calculated pressure to the given pressure
According to the problem, the radiation pressure can also be expressed as:
\[ P = p \times 10^{-7} \, \text{N/m}^2 \]
Setting the two expressions for pressure equal to each other:
\[ 1.5 \times 10^{-6} = p \times 10^{-7} \]

### Step 6: Solve for \( p \)
To find \( p \), we rearrange the equation:
\[ p = \frac{1.5 \times 10^{-6}}{10^{-7}} = 15 \]

### Final Answer
Thus, the value of \( p \) is:
\[ \boxed{15} \]