Question

if P represents radiation pressure , c represents speed of light and Q represents radiation energy striking a unit per second , then non-zero integers x,y and z are such that PxQyCz is dimensionless.x,y,z are the powers of P,Q,C respectively.

Answer 1

Thanks for asking the question.

ANSWER::

Question is from the chapter Unit And Dimensions of Class 11

Dimensions of Radiation Pressure = M1L-1T-2
Dimensions of Speed of Light = M0L1T-1
......
and the answer continues in the picture please refer that.

Hope it helps!

Answer 2

Answer:

Explanation:

Let k=PxSycz .....(i)

k is a dimensionless

Dimensions of k=[M0L0T0]

∴ Dimensions of P =ForceArea=[MLT−2][L2]=[ML−1T−2]

Dimensions of S= EnergyArea× time=[ML2T−2][L2][T]=[MT−3]

Dimensions of c=[LT−1]

Substituting these dimensions in eqn (i), we get

[M0L0T0]=[ML−1T−2]x[MT−3]y[LT−1]z.

Applying the principle of homogeneity of dimensions, we get

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

−x+z=0 ....(iii)

−2x−3y−z=0 ....(iv)

Solving (ii), (iii) and (iv), we get

x=1,y=−1,z=1