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Physics

The velocity $$v$$ of a particle at time$$ t$$ is given by $$\displaystyle v = at + \frac {b} {t + c} $$ where $$a, b$$ and $$c$$ are constants. The dimensions of $$a, b$$ and $$c$$ are respectively :

A
$$ LT^{-2}\, , L $$ and $$\displaystyle T $$
B
$$ L^{2}\, , T $$ and $$\displaystyle LT^{2} $$
C
$$ LT^{2}\, , LT $$ and $$\displaystyle L $$
D
$$ L\, , LT $$ and $$\displaystyle T^{2} $$
Answer & Solution

$$ LT^{-2}\, , L $$ and $$\displaystyle T $$


SOLUTION

According to the principle of dimensional homogenity

Dimension of v = dimension of at  =  dimension of $$\displaystyle  \frac {b} {t +c} $$

Dimension of a =  $$\displaystyle \frac {[v]} {[t]} = \frac {LT^{-2}} {T} = [LT^{-2}] $$

Dimension of b = $$\displaystyle [v] [t] = [LT^{-1}T] = [L] $$ 

Dimension of c = $$\displaystyle  [t] = [T] $$

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