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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

Asked in JEE Main 8th April 2nd Shift 2019 · Expressing a quantity in new base units

Answer: (2) S^1/2I^1/2h⁰

Step-by-step solution

Given: momentum =[MLT⁻¹], with S=[MT⁻²], I=[ML²], h=[ML²T⁻¹].

Write p=S^aI^bh^c and match each base.

Time: -1=-2a-c. Length: 1=2b+2c. Mass: 1=a+b+c.

Trying c=0: the length equation gives b=1/2, the time equation gives a=1/2.

Mass check: 1/2+1/2+0=1, which holds, so p=S^1/2I^1/2h⁰.

Why the other options are wrong

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