Question

If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x, y and z such that Pˣ Qʸ cᶻ is dimensionless, are:

• A. x = 1, y = 1, z = -1
• B. x = 1, y = -1, z = -1
• C. x = -1, y = 1, z = 1
• D. x = 1, y = -1, z = 1

Hint:

Always write dimensions of each physical quantity first and then equate the powers of M, L, T separately to make the expression dimensionless.

Answer 1

The Correct Option is D

Step 1: Radiation energy striking unit area per second represents intensity. [Q] = EnergyArea × Time = ML²T⁻²L²T = MT⁻³
Step 2: Speed of light has dimensions [c] = LT⁻¹
Step 3: Radiation pressure is given by P = (Q)/(c) [P] = MT⁻³LT⁻¹ = ML⁻¹T⁻²
Step 4: For PˣQʸcᶻ to be dimensionless: (ML⁻¹T⁻²)ˣ(MT⁻³)ʸ(LT⁻¹)ᶻ = M⁰L⁰T⁰ Equating powers: aligned M &: x + y = 0
L &: -x + z = 0
T &: -2x -3y - z = 0 aligned
Step 5: Solving: y = -x, z = x Taking x = 1: y = -1, z = 1