An unknown quantity - is expressed - -2ma-log 1-2-ma where m - mass- a - acceleration- - - length The unit of - should be

The correct option is A meter α = 2ma β #160; log 1+ 2βψ #160; ma #160; #160; #160; First find unit of β .The value of log is dimensionl ...

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Standard XII

Physics

Dimensional Analysis

An unknown qu...

Question

An unknown quantity $" α "$ is expressed $α = \frac{2 m a}{β} log (1 + \frac{2 β φ}{m a})$
where $m$ = mass, $a$ = acceleration, $φ$ = length
The unit of $α$ should be

meter

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m / s

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m / s

^{2}

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s

^{- 1}

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Solution

The correct option is A meter
$α = \frac{2 m a}{β} log 1 + \frac{2 β ψ}{m a}$

First find unit of $β$ .

The value of log is dimensionless so dimension of:

$β ψ = m a$

$β (m) = (k g) (m / s e c^{2})$

Unit of $β = \frac{k g}{{s e c}^{2}}$

Unit of $α = \frac{k g . m / {s e c}^{2}}{k g / {s e c}^{2}} = m = m e t e r$

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An unknown quantity "α" is expressed α=2maβlog(1+2βφma)where m = mass, a = acceleration, φ = length The unit of α should be

The correct option is A meterα=2maβlog1+2βψmaFirst find unit of β.The value of log is dimensionless so dimension of:βψ=maβ(m)=(kg)(m/sec2)Unit of β=kgsec2 Unit of α=kg.m/sec2kg/sec2=m=meter

An unknown quantity $" α "$ is expressed $α = \frac{2 m a}{β} log (1 + \frac{2 β φ}{m a})$
where $m$ = mass, $a$ = acceleration, $φ$ = length
The unit of $α$ should be