Q125 / 155 · WBJEE 2016 · Physics

If $x=a t+b t^{2},$ where $x$ is in metre $(\mathrm{m})$ and $t$ is in hour $(\mathrm{h})$, then unit of $b$ will be

  • A
    $\frac{\mathrm{m}^{2}}{\mathrm{h}}$
  • B
    $m$
  • C
    $\frac{m}{h}$
  • Correct answer
    D
    $\frac{m}{h^{2}}$

Solution

Given, $x=a t+b t^{2}$ $\begin{array}{l} {[x]=\left[b t^{2}\right]} \\ \text { Unit of } b=\frac{x}{t^{2}}=\frac{\text { metre }}{(h)^{2}}=\frac{m}{h^{2}} \end{array}$

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

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