# If P represents radiation pressure, c represents the speed of light and Q represents radiation energy striking a unit area per second, then the values

64 views
in Physics
closed

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

1. x = 1, y = 1, z = -1
2. x = 1, y = -1, z = 1
3. x = -1, y = 1, z = 1
4. x = 1, v = 1, z = 1

by (24.2k points)
selected

Correct Answer - Option 2 : x = 1, y = -1, z = 1

CONCEPT:

Principle of homogeneity of dimensions:

• According to this principle, a physical equation will be dimensionally correct if the dimensions of all

the terms occurring on both sides of the equation are the same.

• This principle is based on the fact that only the physical quantities of the same kind can be

• Thus, velocity can be added to velocity but not to force.

EXPLANATION:

Given that, P = pressure, Q = Energy striking per unit area per second, C = speed of light

Let k = PxQyCz....(1)

Dimensions of k = [M0L0T0]

Therefore Dimensions of $Pressure=\frac{Force}{Area}=\frac{MLT^{-2}}{L^2}$ = ML-1T-2

$Q=\frac{Energy}{Area \times time}=\frac{MLT^{-2}}{L^2}=\frac{ML^{2}T^{-2}}{L^{2}T}=MT^{-3}$

$C=LT^{-1}$

Substituting these values in equation (1)

$M^{0}L^{0}T^{0}=[ML^{-1}T^{-2}]^{x}[MT^{-3}]^{y}[LT^{-1}]^{z}$

Applying the principle of homogeneity of dimensions, we get

x + y = 0...(i)

-x + z = 0...(ii)

-2x - 3y - z = 0...(iii)

solving (i),(ii),(iii), we get

x = 1,y = -1,z = 1

The correct x = 1,y = -1,z = 1