Question

If pressure ,velocity of light and per area per second radiation energy are represented by P,C and Q respectively.Then,non-zero integers x,y,z that P^x Q^y C^z is dimensionless,then.........
a) x=1, y=1, z=-1
b) x=1, y=1, z=1
c) x=-1, y=1, z=1
d) none of the above

Answer 1

Given :
P-- Pressure 
C- Velocity
Q--- radiation energy  striking unit area second
[Pˣ Qʸ cᶻ ]=[M⁰ L⁰ T⁰]
∴[M⁰ L⁰ T⁰] =[M¹ L⁻¹  T⁻² ]ˣ  [ M L² T⁻²/L² T  ]ʸ [L T⁻¹ ]ᶻ 
M⁰ L⁰ T⁰=  Mˣ⁺ʸ Lᶻ⁻ˣ T⁻²ˣ⁻³ʸ⁻ᶻ
x+y=0
z-x=0
-2x-3y-z=0
By solving we get :
X=Z
X=-y
so the correct option would be X=1 , Y=-1 and Z=1
It would be None of above   --- option [d] .

I hope it is clear.