The universal gravitational constant G is to be expressed dimensionally in terms of Planck's constant h, length L, mass M and time T. Which of the following expressions has the correct dimensions of G?
Options

Question

The universal gravitational constant G is to be expressed dimensionally in terms of Planck's constant h, length L, mass M and time T. Which of the following expressions has the correct dimensions of G?

Options

G1 Physics · Accepted Answer

The dimensional formula of the universal gravitational constant is [G] = M⁻¹ L³ T⁻². Planck's constant has dimensions [h] = M L² T⁻¹. Now check option B: [h T⁻¹ L M⁻²] = [M L² T⁻¹] × [T⁻¹] × [L] × [M⁻²] = M⁻¹ L³ T⁻². This is exactly the dimensional formula of G. Therefore, [G] = [h T⁻¹ L M⁻²]. Correct option: B.