Question

If P is radiation pressure, c represents speed of light and Q is radiation energy striking a unit area per second, then non zero integers x, y and z such that $P^x{Q}^y{C}^z$ 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

Answer 1

The correct option is B x = 1, y = –1, z = 1

Pressure $P=\frac{F}{A}=\frac{\left[M^1{L}^1{T}^{-2}\right]}{\left[L^2\right]}=\left[M^1{L}^{-1}{T}^{-2}\right]$
Speed of light $C=\left[L^1{T}^{-1}\right]$
Radiation energy $Q=\frac{E}{At}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^{2}T\right]}=\left[M{T}^{-3}\right]$.
$P^x{Q}^y{C}^z=[M^1{L}^{-1}{T}^{-2}{]}^x\times [M{T}^{-3}{]}^y[L^1{T}^{-1}{]}^z$
$\left[M^0{L}^0{T}^0\right]=[M^1{L}^{-1}{T}^{-2}{]}^x\times [M{T}^{-3}{]}^y[L^1{T}^{-1}{]}^z$
On comparing the powers of M, L and T
x + y = 0
-x + z = 0
- 2x - 3y - z = 0
All these conditions are satisfied by option (B).