Physics And Measurement Question 29

Question: If the dimensions of length are expressed as $ G^{x}c^{y}h^{z} $ ; where $ G,c $ and $ h $ are the universal gravitational constant, speed of light and Planck’s constant respectively, then

[IIT 1992]

Options:

A) $ x=\frac{1}{2},y=\frac{1}{2} $

B) $ x=\frac{1}{2},z=\frac{1}{2} $

C) $ y=\frac{1}{2},z=\frac{3}{2} $

D) $ y=-\frac{3}{2},z=\frac{1}{2} $

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Answer:

Correct Answer: B

Solution:

Length µ Gxcyhz L= $ {{[{{M}^{-1}}L^{3}{{T}^{-2}}]}^{x}} $

$ {{[L{{T}^{-1}}]}^{y}}{{[ML^{2}{{T}^{-1}}]}^{z}} $

By comparing the power of M, L and T in both sides we get $ -x+z=0 $ , $ 3x+y+2z=1 $

and $ -2x-y-z=0 $ By solving above three equations we get

$ x=\frac{1}{2},y=-\frac{3}{2},z=\frac{1}{2} $



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