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in Physics by (24.2k points)

If p represents the pressure, c represent the velocity of lights and q the radiation energy per unit time., then calculate non-zero integers x, y and z such that px qz cz is dimensionless.

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Dimensions of p = pressure = [ML-1T-2]

Dimensions of p = Energy/Area x time = [ML0T-3]

Dimensions of c = speed = [LT-1]

Hence px qy cz = [ML-1T-2]x [ML0T-3]y [LT-1]z

Now,px qy cz will be dimensionless if

x + y = 0........(i)

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

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

These equations have infinite solution.One of the solution is x = 1, y = -1, and  z =1, so that px qy cz is dimensionless.

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