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Question:

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :

S3/2I1/2h

S1/2I1/2h

S1/2I3/2h−

S1/2I1/2h−

Solution:

Correct option is B. S1/2I1/2h
p = kSaIbhc
where k is dimensionless constant
MLT-1 = (MT-2)a(ML2)b(ML2T-1)c
a + b + c = 1
2b + 2c = 1
-2a - c = -1
Solving these equations, we get:
a = 1/2
b = 1/2
c = 0
Therefore, the dimensional formula for linear momentum is S1/2I1/2h0 = S1/2I1/2h