Q98 / 200 · NEET 2006 · Physics

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

  • A
    L, LT and $\mathrm{LT}^2$
  • Correct answer
    B
    $\mathrm{LT}^{-2}, \mathrm{~L}$ and $\mathrm{T}$
  • C
    $\mathrm{L}^2, \mathrm{~T}$ and $\mathrm{LT}^2$
  • D
    $\mathrm{LT}^2$, LT and L.

Solution

Using principle of homogeniety. Dimension of $v=$ Dimension of $a t=$ Dimenstion of $\frac{b}{t+c}$ $\begin{array}{l} \therefore a t =\left[\mathrm{LT}^{-1}\right] \\ \Rightarrow |a| =\frac{\left[\mathrm{LT}^{-1}\right]}{[\mathrm{T}]}=\left[\mathrm{LT}^{-2}\right] \\ \text {And } \frac{[b]}{[t]} =\left[\mathrm{LT}^{-1}\right] \\ {[b]} =\left[\mathrm{LT}^{-1}\right][\mathrm{T}]=[\mathrm{L}] \\ \text {And } c =\mathrm{T} \\ \Rightarrow c =[\mathrm{T}] \end{array}$

Hence, the correct answer is option: 'B'.

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