First slide

Dimensions of physical quantities

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 a, b and c are such that $p^{a} q^{b} c^{c}$ is dimensionless, then

Moderate

A

a = 1, b = 1, c = -1
B

a = 1, b = -1, c = 1
C

a = -1, b = 1, c = 1
D

a = 1, b = 1, c = 1

Solution

Here, $[M^{0} L^{0} T^{0}] = {[M L^{- 1} T^{- 2}]}^{a} {[M L^{- 3}]}^{b} {[L T^{- 1}]}^{c}$
or $[M^{0} L^{0} T^{0}] = [M^{a + b} L^{- a + c} T^{- 2 a - 3 b - c}]$
Comparing powers of M, L and T, we get
a + b = 0,-a + c = 0,-2a -3b = 0
Solving, a =1, b = -1, c =1

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