Question

A pulse of light of duration 50 ns is absorbed completely by a small object initially at rest. Power of the pulse is 60 mW and speed of light is \( 3 \times 10^8 \) m/s. The final momentum of the object is:

• A. \( 1.0 \times 10^{-17} \) kg m/s
• B. \( 3.0 \times 10^{-17} \) kg m/s
• C. \( 1.0 \times 10^{-16} \) kg m/s
• D. \( 3.0 \times 10^{-16} \) kg m/s

Hint:

To calculate the momentum of an object absorbed with light, use the energy and speed of light relation: \( p = \frac{E}{c} \).

Answer 1

The Correct Option is C

Given that the energy of the pulse \( E = P \times t \), where \( P \) is the power of the pulse and \( t \) is the duration: \[ E = 60 \, \text{mW} \times 50 \, \text{ns} = 60 \times 10^{-3} \, \text{W} \times 50 \times 10^{-9} \, \text{s} = 3 \times 10^{-15} \, \text{J} \] Now, the momentum \( p \) of the object is given by the equation \( p = \frac{E}{c} \), where \( c = 3 \times 10^8 \, \text{m/s} \) is the speed of light: \[ p = \frac{3 \times 10^{-15} \, \text{J}}{3 \times 10^8 \, \text{m/s}} = 1.0 \times 10^{-16} \, \text{kg m/s} \] Thus, the final momentum of the object is \( 1.0 \times 10^{-16} \, \text{kg m/s} \).