Q.

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

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a

hcG

b

Gch32

c

hGc32

d

hGc52

answer is C.

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Detailed Solution

Let dimensions of length l ∝ hxGyczM0L1T0 = (ML2T-1)x(M-1L3T-2)y(LT-1)z= Mx-yL2x+3y+zT-x-2y-zEquating  dimensions on left and right hand side,x- y = 0                    2x+3y+z= 1     -x-2y-z=0  ⇒x = 12; y = 12; z = -32                 ⇒l ∝ hGc32
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Planck's constant (h), speed of light in vaccum c and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?