JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Units & Measurement

E, L, M

and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of

P

in the formula

P = E L^{2} M^{- 5} G^{- 2}

are :-

Answer: (A)

Solution

The four quantities have dimensions

[E] = [M L^{2} T^{- 2}]

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

[M] = [M]

and

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

. Substituting into

P = E L^{2} M^{- 5} G^{- 2}

[P] = [M L^{2} T^{- 2}] [M^{2} L^{4} T^{- 2}] [M^{- 5}] [M^{2} L^{- 6} T^{4}]

The exponents add to

1 + 2 - 5 + 2 = 0

for mass,

2 + 4 - 6 = 0

for length and

- 2 - 2 + 4 = 0

for time, so

[P] = [M^{0} L^{0} T^{0}]

and

P

is a dimensionless quantity.

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Single correct option