The total momentum delivered (for complete absorption) of energy flux of `30 W//cm^2` falling on a non-reflecting surface of surface area `40 cm^2` at normal incidence, during 30 minutes is found be `N xx 10^(-4)` SI units. The value of N is ____

Explanation

To solve the problem, we need to calculate the total momentum delivered by the energy flux falling on a non-reflecting surface. Let's break it down step by step.

### Step 1: Understand the given values
- Energy flux (intensity), \( I = 30 \, \text{W/cm}^2 \)
- Surface area, \( A = 40 \, \text{cm}^2 \)
- Time, \( T = 30 \, \text{minutes} \)

### Step 2: Convert time into seconds
Since we need to work in SI units, we convert time from minutes to seconds:
\[ T = 30 \, \text{minutes} \times 60 \, \text{seconds/minute} = 1800 \, \text{seconds} \]

### Step 3: Calculate the energy carried by the light
The energy \( U \) carried by the light can be calculated using the formula:
\[ U = I \times A \times T \]
Substituting the values:
\[ U = 30 \, \text{W/cm}^2 \times 40 \, \text{cm}^2 \times 1800 \, \text{s} \]

### Step 4: Calculate \( U \)
Calculating \( U \):
\[ U = 30 \times 40 \times 1800 = 2160000 \, \text{J} \]

### Step 5: Calculate the momentum delivered
The momentum \( P \) delivered by the energy can be calculated using the formula:
\[ P = \frac{U}{c} \]
Where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 6: Convert \( U \) to SI units
Since \( U \) is in Joules, we can directly use it in the momentum formula:
\[ P = \frac{2160000 \, \text{J}}{3 \times 10^8 \, \text{m/s}} \]

### Step 7: Calculate \( P \)
Calculating \( P \):
\[ P = \frac{2160000}{3 \times 10^8} = 7.2 \times 10^{-3} \, \text{kg m/s} \]

### Step 8: Express \( P \) in the required format
We need to express \( P \) in the form \( N \times 10^{-4} \):
\[ P = 72 \times 10^{-4} \, \text{kg m/s} \]

### Step 9: Identify the value of \( N \)
From the above expression, we can see that:
\[ N = 72 \]

### Final Answer
The value of \( N \) is \( 72 \).

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