If mass is written as $\mathrm{m}=\mathrm{k} \mathrm{c}^{\mathrm{P}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Units & Measurement

If mass is written as

m = k c^{P} G^{- 1/2} h^{1/2}

then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

Answer: (A)

Writing

m = k c^{P} G^{- 1/2} h^{1/2}

with

[c] = L T^{- 1}

[G] = M^{- 1} L^{3} T^{- 2}

[h] = M L^{2} T^{- 1}

, and matching dimensions on both sides:

[M^{1} L^{0} T^{0}] = [L T^{- 1}]^{P} [M^{- 1} L^{3} T^{- 2}]^{- 1/2} [M L^{2} T^{- 1}]^{1/2}

[M^{1} L^{0} T^{0}] = [L^{P} T^{- P}] [M^{1/2} L^{- 3/2} T^{1}] [M^{1/2} L^{1} T^{- 1/2}]

Collecting powers of

L

0 = P - \frac{3}{2} + 1

P = \frac{1}{2}

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option