A small object at rest, absorbs a light pulse of power 20 mW and duration 300 ns. Assuming speed of light as 3 × 10⁸ m / s, the momentum of the object becomes equal to :

Solution

Physics sir · 3 steps

Light carries momentum E/c; find the pulse's energy, and a full absorber takes all of it.

1. Energy of the pulse. Energy is power times time: E = (20 × 10⁻³ W) × (300 × 10⁻⁹ s) = 6 × 10⁻⁹ J.
2. Momentum of light. Light of energy E carries momentum E/c. The object starts at rest and absorbs the whole pulse, so momentum conservation gives it all of that momentum.

   p = E/c = (6 × 10⁻⁹ J)/(3 × 10⁸ m s⁻¹) = 2 × 10⁻¹⁷ kg m s⁻¹

3. So. The object's momentum becomes 2 × 10⁻¹⁷ kg m s⁻¹, which is option (d).

The idea to keep. For light, momentum is energy divided by c. A perfect absorber picks up E/c, while a perfect reflector picks up 2E/c because the light's momentum reverses.

Answer from the NTA final answer key. Solution by PrepWiser.