A pulse of light of duration `100 ns` is absorbed completely by a small object initially at rest. Power of the pulse is `30 m W` and the speed of light is `3xx10 ms^(-1)`. The final momentum of the object is :

Options

A. `0.3xx10^(17) kg ms^(-1)`
B. `1.0xx10^(17) kg ms^(-1)`
C. `3.0xx10^(-17) kg ms^(-1)`
D. `9.0xx10^(-17)kg ms^(-1)`

Explanation

To find the final momentum of the object after absorbing a pulse of light, we can follow these steps:

### Step 1: Understand the relationship between power, energy, and time
The energy \( E \) of the light pulse can be calculated using the formula:
\[ E = \text{Power} \times \text{Time} \]
Given that the power of the pulse is \( 30 \, \text{mW} = 30 \times 10^{-3} \, \text{W} \) and the duration of the pulse is \( 100 \, \text{ns} = 100 \times 10^{-9} \, \text{s} \), we can calculate the energy.

### Step 2: Calculate the energy of the light pulse
Substituting the values into the energy formula:
\[ E = (30 \times 10^{-3} \, \text{W}) \times (100 \times 10^{-9} \, \text{s}) = 30 \times 10^{-3} \times 100 \times 10^{-9} = 3 \times 10^{-12} \, \text{J} \]

### Step 3: Calculate the momentum of the light pulse
The momentum \( p \) of the light can be calculated using the formula:
\[ p = \frac{E}{c} \]
where \( c \) is the speed of light, given as \( 3 \times 10^8 \, \text{m/s} \).

### Step 4: Substitute the energy and speed of light into the momentum formula
Substituting the values we calculated:
\[ p = \frac{3 \times 10^{-12} \, \text{J}}{3 \times 10^8 \, \text{m/s}} = 10^{-20} \, \text{kg m/s} \]

### Step 5: Determine the final momentum of the object
Since the object absorbs the momentum of the light pulse, the final momentum of the object is:
\[ p_{\text{final}} = 10^{-20} \, \text{kg m/s} \]

### Final Answer
The final momentum of the object is \( 10^{-20} \, \text{kg m/s} \).

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