A pulse of light of duration `100ns` is absorbed completely by a small object initially at rest power of the pulse is `30 mW` and the speed of light is `3 xx 10^(8) ms^(-1)` The final momentum of the object is

Options

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

Explanation

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

### Step 1: Calculate the Energy of the Light Pulse
The energy \( E \) of the light pulse can be calculated using the formula:
\[ E = P \times t \]
where:
- \( P \) is the power of the pulse (in watts),
- \( t \) is the duration of the pulse (in seconds).

Given:
- \( P = 30 \, \text{mW} = 30 \times 10^{-3} \, \text{W} \)
- \( t = 100 \, \text{ns} = 100 \times 10^{-9} \, \text{s} \)

Substituting the values:
\[ E = (30 \times 10^{-3}) \times (100 \times 10^{-9}) = 30 \times 100 \times 10^{-12} = 3 \times 10^{-10} \, \text{J} \]

### Step 2: Calculate the Momentum of the Light Pulse
The momentum \( p \) of the light pulse can be calculated using the formula:
\[ p = \frac{E}{c} \]
where:
- \( c \) is the speed of light.

Given:
- \( c = 3 \times 10^{8} \, \text{m/s} \)

Substituting the energy calculated in Step 1:
\[ p = \frac{3 \times 10^{-10}}{3 \times 10^{8}} = 1 \times 10^{-18} \, \text{kg m/s} \]

### Step 3: Final Momentum of the Object
Since the object is initially at rest and absorbs the entire momentum of the light pulse, the final momentum of the object will be equal to the momentum of the light pulse:
\[ \text{Final Momentum of the Object} = 1 \times 10^{-18} \, \text{kg m/s} \]

### Conclusion
The final momentum of the object after absorbing the light pulse is:
\[ \boxed{1 \times 10^{-18} \, \text{kg m/s}} \]

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