In relation A = , the quantity A, B and C are expressed in units of N kg⁻¹ s³, ms² and m² s⁻¹, respectively.If p and q are constants, find the values of p and q.

Correct option is B

Correct answer is B
Explanation:
From the given units:
A = N kg-1s3 => Force per mass per time cubed.
B = m.s2 => Distance per time squared.
C = m2s-1 => Area per time.
To balance the units in A = BpCq, consider the dimensional analysis:
The unit of A is derived from multiplying the units of B and C raised to powers p and q:
Unit of A = (Unit of B)p × (Unit of C)q.
Substitute the units:
N kg-1s3 = (m.s2)p × (m2s-1)q.
Breaking down N (Newton): N = kg.m.s-2, so:
kg.m.s-2 × kg-1s3 => m.s1.
Equating powers of m, s, and kg:
For m: 1 = p + 2q.
For s: 1 = 2p - q.
For kg: kg terms cancel out.
Solve the equations:
From 1 = p + 2q => q = (1 - p)/2.
Substitute q in 1 = 2p - q:
1 = 2p - (1 - p)/2 => 2 = 4p - 1 + p => 5p = 3.
p = 3/5.
Substitute p = 3/5 in q = (1 - p)/2:
q = (1 - 3/5)/2 => q = 2/5 × 1/2 => q = 1/5.