If the force is given by $F=a t+b t^2$ with $t$ as time. The dimensions of $a$ and $b$ are

If the force is given by $F=a t+b t^2$ with $t$ as time. The dimensions of $a$ and $b$ are
  1. $\left[\mathrm{MLT}^{-4}\right],\left[\mathrm{MLT}^{-2}\right]$
  2. $\left[\mathrm{MLT}^{-3}\right],\left[\mathrm{MLT}^{-4}\right]$
  3. $\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right],\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
  4. $\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right],\left[\mathrm{ML}^3 \mathrm{~T}^{-4}\right]$

Solution

Dimension of $a t=$ Dimension of $F$ $[a t]=[F]$ $[a]=\left[\frac{F}{t}\right]$ $[a]=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{~T}}\right]$ $[a]=\left[\mathrm{MLT}^{-3}\right]$ Dimension of $b t^2=$ Dimension of $F$ $\left[b t^2\right]=[F]$ $[b]=\left[\frac{F}{t^2}\right]$ $[b]=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{~T}^2}\right]$ $[b]=\left[\mathrm{MLT}^{-4}\right]$

Asked in: AP EAMCET 2010

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