Question

If P represents radiation pressure, c represents speed of light and Q represents 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

By substituting the dimension of given quantities

$\left[M{L}^{-1}{T}^{-2}{]}^x\right[M{T}^{-3}{]}^y[L{T}^{-1}{]}^z=[MLT{]}^0$

By comparing the power of M,L,T in both sides x + y = 0 .....(i)

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

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

The only values of x,y,z satisfying ((i),(ii) and (iii) corresponds to (b).