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} $
Show Answer
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} $
