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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousMedium2 minQB

PhysicsMediumsingle choice

$\frac{α}{t ^{2}} = F v + \frac{β}{x ^{2}}$ . Find dimension formula for $[α]$ and $[β]$ (here $t =$ time, $F =$ force, $v =$ velocity, $x =$ distance )

Options:

Answer:

Solution:

$[F v] = [M L T^{- 2}] [L T^{- 1}]$
$= [M L^{2} T^{- 3}]$ , so
$\frac{[ β ]}{[ x ^{2} ]}$
$= [M L^{2} T^{- 3}]$ giving
$[β] = [M L^{4} T^{- 3}]$ , and
$\frac{[ α ]}{[ t ^{2} ]}$
$= [M L^{2} T^{- 3}]$ giving
$[α] = [M L^{2} T^{- 1}]$ .

Stream:JEESubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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