If dimensions of length are expressed as GxCyhz where G, C and h are universal gravitational constant, speed of light and Planck's constant respectively. Then
x=z
x=y
z=1/2
y=−3/2
A
x=y
B
x=z
C
y=−3/2
D
z=1/2
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Solution
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(M0L1T0)αGxlyhz
G=(M1L1T−2)M2×(L2)=M−1L3T−2
C=LT−1
h=EnergyCλ=M1L2T−2LT−1L=M1L2T−1
M0L1T0=(M−1L3T−2)x(LT−1)y(M1L2T−1)z
−x+z=0,3x+y+2z=1,−2x−y−z=0
x=z
⇒5x+y=1
y=−3/2
x=1/2
z=1/2
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