JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Units & Measurement

Dimensions of universal gravitational constant (G) in terms of Planck's constant (

h

), distance (

L

), mass (

M

) and time (

T

) are ____.

Answer: (B)

Solution

Writing

[G] = [h]^{a} [L]^{b} [M]^{c} [T]^{d}

with

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

and

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

, the powers of

M

L

and

T

must match:

a + c = - 1

2 a + b = 3

and

- a + d = - 2

. Taking

a = 1

gives

c = - 2

b = 1

and

d = - 1

. Therefore the dimensions of the universal gravitational constant are

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

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option