Question:
Light with an energy flux of \(20 \, W \, cm^{-2}\) falls on a non-reflecting surface at normal incidence. If the surface has an area of \(25 \, cm^2\), then the total momentum delivered for complete absorption during a 15 minute time span is:
Light with an energy flux of \(20 \, W \, cm^{-2}\) falls on a non-reflecting surface at normal incidence. If the surface has an area of \(25 \, cm^2\), then the total momentum delivered for complete absorption during a 15 minute time span is:
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For absorption of light: momentum delivered = \(E/c\).
Updated On: Jun 20, 2026
- \(1 \times 10^{-3} \, kg\, m\, s^{-1}\)
- \(1.8 \times 10^{-3} \, kg\, m\, s^{-1}\)
- \(2 \times 10^{-3} \, kg\, m\, s^{-1}\)
- \(1.5 \times 10^{-3} \, kg\, m\, s^{-1}\)
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The Correct Option is D
Solution and Explanation
Step 1: Convert intensity into SI units.
\[ I = 20 \, W\, cm^{-2} = 20 \times 10^4 \, W\, m^{-2} = 2 \times 10^5 \, W\, m^{-2} \]
Step 2: Convert area.
\[ A = 25 \, cm^2 = 25 \times 10^{-4} = 2.5 \times 10^{-3} \, m^2 \]
Step 3: Power incident on surface.
\[ P = IA = 2 \times 10^5 \times 2.5 \times 10^{-3} = 500 \, W \]
Step 4: Time conversion.
\[ t = 15 \, min = 900 \, s \]
Step 5: Energy delivered.
\[ E = Pt = 500 \times 900 = 4.5 \times 10^5 \, J \]
Step 6: Momentum delivered.
For complete absorption: \[ p = \frac{E}{c} \] \[ p = \frac{4.5 \times 10^5}{3 \times 10^8} = 1.5 \times 10^{-3} \] \[ \boxed{1.5 \times 10^{-3} \, kg\, m\, s^{-1}} \]
\[ I = 20 \, W\, cm^{-2} = 20 \times 10^4 \, W\, m^{-2} = 2 \times 10^5 \, W\, m^{-2} \]
Step 2: Convert area.
\[ A = 25 \, cm^2 = 25 \times 10^{-4} = 2.5 \times 10^{-3} \, m^2 \]
Step 3: Power incident on surface.
\[ P = IA = 2 \times 10^5 \times 2.5 \times 10^{-3} = 500 \, W \]
Step 4: Time conversion.
\[ t = 15 \, min = 900 \, s \]
Step 5: Energy delivered.
\[ E = Pt = 500 \times 900 = 4.5 \times 10^5 \, J \]
Step 6: Momentum delivered.
For complete absorption: \[ p = \frac{E}{c} \] \[ p = \frac{4.5 \times 10^5}{3 \times 10^8} = 1.5 \times 10^{-3} \] \[ \boxed{1.5 \times 10^{-3} \, kg\, m\, s^{-1}} \]
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