Time (T) , velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mas

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1.Units, Dimensions and Measurement

hard

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

A

$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,h} \right]$

B

$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^2}\,h} \right]$

C

$\left[ M \right] = \left[ {{T^{ - 1}}\,{C^{ - 2}}\,{h^{ - 1}}} \right]$

D

$\left[ M \right] = \left[ {T\,{C^{ - 2}}\,h} \right]$

(JEE MAIN-2017)

Solution

Let mass related as $M \propto \,{T^x}{C^y}{h^z}$
${M^1}{L^0}{T^0} = {\left( T \right)^x}{\left( {{L^1}{T^{ – 1}}} \right)^y}{\left( {{M^1}{L^2}{T^{ – 1}}} \right)^z}$
${M^1}{L^0}{T^0} = {M^z}{L^{y + 2z}} + {T^{x – y – z}}$
$z = 1$
$y + 2z = 0$ $x – y – z = 0$
$y = – 2$ $x + 2 – 1 = 0$
$M = \left[ {{T^{ – 1}}{C^{ – 2}}{h^1}} \right]$

Standard 11

Physics

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