Physics Q26 – JEE-MAIN 2026

Home Physics Units & MeasurementsQuestion #546

Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are _______.

Clue 1 of 3: Fundamental Dimensions

Recall the fundamental dimensions of universal gravitational constant ( $G$ ) and Planck's constant ( $h$ ) in terms of mass ( $M$ ), length ( $L$ ), and time ( $T$ ).

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Step 1: Determine the dimensions of G and h✦ Active

The universal gravitational constant $G$ is derived from Newton's Law of Gravitation, $F = G \frac{m_{1} m_{2}}{r^{2}}$ . Rearranging for $G$ , we get $G = \frac{F r^{2}}{m_{1} m_{2}}$ . The dimensions of force $F$ are $[M L T^{- 2}]$ , distance $r$ are $[L]$ , and mass $m$ are $[M]$ . Therefore, the dimensions of $G$ are:

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

Planck's constant $h$ is derived from the energy of a photon, $E = h ν$ , where $ν$ is frequency. Rearranging for $h$ , we get $h = \frac{E}{ν}$ . The dimensions of energy $E$ are $[M L^{2} T^{- 2}]$ and frequency $ν$ are $[T^{- 1}]$ . Therefore, the dimensions of $h$ are:

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

Step 2: Evaluate the dimensions of each option○ Expand

We need to find an option that, when simplified, yields the dimensions of $G$ , which are $[M^{- 1} L^{3} T^{- 2}]$ . Let's check Option 2: $[h T^{- 1} L M^{- 2}]$ . Substitute the dimensions of $h$ into this expression:

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

Combine the powers of M, L, and T:

Power of M: 1 - 2 = - 1 Power of L: 2 + 1 = 3 Power of T: - 1 - 1 = - 2

So, Option 2 simplifies to $[M^{- 1} L^{3} T^{- 2}]$ .

💡 Teacher's Secret Hint

Carefully combine the exponents for each fundamental dimension (M, L, T) when multiplying dimensional formulas.

Step 3: Compare with the dimensions of G○ Expand

The calculated dimensions for Option 2, $[M^{- 1} L^{3} T^{- 2}]$ , exactly match the dimensions of the universal gravitational constant $G$ derived in Step 1. Therefore, Option 2 is the correct answer.

💡 Teacher's Secret Hint

If the first option doesn't match, continue checking the remaining options systematically.

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Physics Question 26 – JEE-MAIN 2026

Clue 1 of 3: Fundamental Dimensions

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