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

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

Unit of P is $Ws/m=\left[M^1{T}^{-3}\right]$.

Unit of C is $m/s=\left[M^0{L}^1{T}^1\right]$.

Unit of Q is $W/m^2=\left[M^1{L}^2{T}^{-2}\right]$.

Hence putting these units in $P^x{Q}^y{C}^z$ and equating the powers of fundamental units to 0, we get $x=1$, $y=-1$ and $z=1$.