Question

The dimensions, of the term, Z = h⁴ CG^-1

(h = Planck’s constant, C = velocity of light, G = universal gravitational constant) equal M² . The value of a, in this term, equals

(1) (4)

(2) (3)

(3) (2)

(4) (1)

Answer 1

(4) (1)

We have,

[h] (= energy x time) = [ML²T^-1]

[G] = (Force x distance²/mass²) = [M^-1L³T^-2]

[C] = (Velocity) = [LT^-1]

∴ From the given relation, we get

[M²] = [ML²T^-1]^a [LT^-1] [M^-1L³T^-2]^-1

These give, 

a+1 = 2; 2a+1–3 = 0; -a -1+2 = 0 

The value of, a, consistent with all these relations, is a = +1