Question:
A pulse of radiation is absorbed by an object initially at rest for \(10^{-4}\, s\). If the power of the pulse is \(9 \times 10^{-3}\, W\), then the total momentum of the object received is.
(Speed of light in vacuum \(c = 3 \times 10^8\, m\,s^{-1}\))
A pulse of radiation is absorbed by an object initially at rest for \(10^{-4}\, s\). If the power of the pulse is \(9 \times 10^{-3}\, W\), then the total momentum of the object received is.
(Speed of light in vacuum \(c = 3 \times 10^8\, m\,s^{-1}\))
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For electromagnetic waves, momentum is always \(p = E/c\), and energy is \(E = Pt\).
Updated On: Jul 18, 2026
- \(3 \times 10^{8}\, kg\, m\, s^{-1}\)
- \(3 \times 10^{13}\, kg\, m\, s^{-1}\)
- \(3 \times 10^{-15}\, kg\, m\, s^{-1}\)
- \(3\, kg\, m\, s^{-1}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding radiation momentum relation.
Electromagnetic radiation carries momentum related to its energy by: \[ p = \frac{E}{c} \] where \(E\) is energy and \(c\) is speed of light.
Step 2: Relating power and energy.
Power is defined as: \[ P = \frac{E}{t} \Rightarrow E = Pt \]
Step 3: Substitute given values.
\[ P = 9 \times 10^{-3}\, W,\quad t = 10^{-4}\, s \] \[ E = 9 \times 10^{-3} \times 10^{-4} = 9 \times 10^{-7}\, J \]
Step 4: Compute momentum of radiation.
\[ p = \frac{E}{c} = \frac{9 \times 10^{-7}}{3 \times 10^{8}} \]
Step 5: Simplify.
\[ p = 3 \times 10^{-15}\, kg\, m\, s^{-1} \]
Step 6: Final conclusion.
Thus, momentum received by object is: \[ \boxed{3 \times 10^{-15}\, kg\, m\, s^{-1}} \]
Electromagnetic radiation carries momentum related to its energy by: \[ p = \frac{E}{c} \] where \(E\) is energy and \(c\) is speed of light.
Step 2: Relating power and energy.
Power is defined as: \[ P = \frac{E}{t} \Rightarrow E = Pt \]
Step 3: Substitute given values.
\[ P = 9 \times 10^{-3}\, W,\quad t = 10^{-4}\, s \] \[ E = 9 \times 10^{-3} \times 10^{-4} = 9 \times 10^{-7}\, J \]
Step 4: Compute momentum of radiation.
\[ p = \frac{E}{c} = \frac{9 \times 10^{-7}}{3 \times 10^{8}} \]
Step 5: Simplify.
\[ p = 3 \times 10^{-15}\, kg\, m\, s^{-1} \]
Step 6: Final conclusion.
Thus, momentum received by object is: \[ \boxed{3 \times 10^{-15}\, kg\, m\, s^{-1}} \]
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