Average force exerted on a non-reflecting surface at normal incidence is 2.4 × 10⁻⁴ N. If 360 W / cm² is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

Solution

Physics sir · 4 steps

For an absorbing surface, force is just intensity times area divided by c, so the 90 minutes do not matter.

1. Absorbing surface. Light carries momentum p = U/c. A non-reflecting surface absorbs it all, so the force on it is the momentum delivered per second, F = P/c = IA/c.

   F = IA/c ⇒ A = Fc/I

2. Convert the flux. 1 cm² = 10⁻⁴ m², so I = 360 W cm⁻² = 3.6 × 10⁶ W m⁻².
3. Put in numbers. A = (2.4 × 10⁻⁴ × 3 × 10⁸)/(3.6 × 10⁶) = (7.2 × 10⁴)/(3.6 × 10⁶) = 0.02 m². The time of 1 hour 30 minutes is not needed, because force is a rate and does not depend on how long the light shines.
4. So. The area of the surface is 0.02 m², option (d).

The idea to keep. Radiation force is IA/c for an absorbing surface and 2IA/c for a perfect reflector. A given time duration is a distractor unless the question asks for total momentum or energy.

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