The velocity of a body is given by the equation $v=\frac{b}{t}+c t^{2}+d t^{3}$ The dimensional formula of…

The velocity of a body is given by the equation $v=\frac{b}{t}+c t^{2}+d t^{3}$
The dimensional formula of $b$ is
  1. $\left[M^{0} L T^{0}\right]$
  2. $\left[M^{0} T^{0}\right]$
  3. $\left[M^{0} L^{0} T\right]$
  4. $\quad M L T^{-1}$

Solution

In the equation, left hand side has the dimension of velocity. Thus, from the principle of homogeneity each term in the right hand side should have the dimensions of velocity.
$\left[\frac{b}{t}\right]=[v]_{\mathrm{o}}[b]=[v t]=[L]$ undefined

Asked in: JEE Mains - Units and Dimensions - Test 2

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