A dimensionless quantity is constructed in te | vedclass

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Question

For the quantity to be dimensionless

$e ^\alpha \varepsilon_0^\beta h ^\gamma c ^{ d }= M ^0 L ^0 T ^0 A ^0$

$\Rightarrow( AT )^\alpha\left( M ^

Vedclass · Accepted Answer

$(2 n,-n,-n,-n)$

Vedclass · Answer

For the quantity to be dimensionless

$e ^\alpha \varepsilon_0^\beta h ^\gamma c ^{ d }= M ^0 L ^0 T ^0 A ^0$

$\Rightarrow( AT )^\alpha\left( M ^{-1} L ^{-3} T ^4 A ^2ight)^\beta\left( ML ^2 T ^{-1}ight)^\gamma\left( LT ^{-1}ight)^\delta= A ^0 M ^0 L ^0 T ^0$

$	herefore \alpha+2 \beta=0, \alpha+4 \beta-\gamma-\delta=0,-\beta+\gamma=0 \&-3 \beta+2 \gamma+\delta=0$

$	herefore \alpha=-2 \beta, \beta=\gamma \& \gamma=\delta$

$	herefore$ Option $(A)$ satisfies the given condition

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