Basic Maths and Units and DimensionsEasy

Question

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Options

A.

hGC32

B.

hGC52

C.

hcG

D.

Gch32

Solution

L ∝ hacbGc
[L]1 = [M1L2T-1]2 [LT-1]b[M-1L3T-2]c
Solving,
a=12, C=12, b=-32
⇒ L=hGc32

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