If dimensions of length are expressed as {G^x}{c^y}{h^z} ; where G,,c and h are universal gravitatio

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1.Units, Dimensions and Measurement

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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

A

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

B

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

C

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

D

$(b)$ and $(c)$ both

(IIT-1992)

Solution

(d) Length $\propto$ $G^{x}c^{y}h^{z}$

$L= {[{M^{ – 1}}{L^3}{T^{ – 2}}]^x}\,$${[L{T^{ – 1}}]^y}{[M{L^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

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

Standard 11

Physics

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