Question

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

• A. $\left[LT^{-2}\right]$, $\left[L\right]$ and $\left[T\right]$
• B. $\left[L^{2}\right]$, $\left[T\right]$ and $\left[LT^{2}\right]$
• C. $\left[LT^{2}\right]$, $\left[LT\right]$ and $\left[L\right]$
• D. $\left[L\right]$, $\left[LT\right]$ and $\left[T^{2}\right]$

Answer 1

Answer: (A)

$\left[LT^{-2}\right]$, $\left[L\right]$ and $\left[T\right]$

Answer 2

$v = at +\frac{ b }{ t + c }$
$\Rightarrow[ c ][ t ]= T$ ;
[v]=[at]
$\Rightarrow[ a ]=\frac{[ V ]}{[ t ]}= LT ^{-2}$
${[ b ]=\left( LT ^{-1}\right) T = L }$