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If mass is written as m=k c^PG^-1/2h^1/2 then the value of P will be: (Constants have their usual meaning with k, a dimensionless constant)

Asked in JEE Main 30th Jan 2nd Shift 2024 · Expressing a quantity in new base units

Answer: (2) 1/2

Step-by-step solution

Given: c=[LT⁻¹], G=[M⁻¹L³T⁻²], h=[ML²T⁻¹].

G^-1/2=[M^1/2L^-3/2T] and h^1/2=[M^1/2LT^-1/2].

Mass: 1/2+1/2=1, which already balances.

Length: 0=P-3/2+1, so P=1/2.

Time check: -P+1-1/2=0 gives P=1/2 as well, so the solution is consistent.

Why the other options are wrong

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