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Question: Given : X = (Gh/c<sup>3</sup>)<sup>1/2</sup>, where G, h and c are gravitational constant, Planck's ...

Given : X = (Gh/c3)1/2, where G, h and c are gravitational constant, Planck's constant and the velocity of light respectively. Dimensions of X are the same as those of-

A

(a) Mass

A

(b) Time

A

(c) Length

A

(d) Acceleration

Explanation

Solution

(c)

Sol. X = (GhC3)1/2\left( \frac{Gh}{C^{3}} \right)^{1/2} = [M−1L3T−2×M1L2T−1L3T−3]1/2\left\lbrack \frac{M^{- 1}L^{3}T^{- 2} \times M^{1}L^{2}T^{- 1}}{L^{3}T^{- 3}} \right\rbrack^{1/2}