Distance travelled by a particle at any instant ' $t$ ' can be represented as…

Distance travelled by a particle at any instant ' $t$ ' can be represented as $\mathrm{S}=\mathrm{A}(\mathrm{t}+\mathrm{B})+\mathrm{Ct}^{2} .$ The
dimensions of $\mathrm{B}$ are
  1. $\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]$
  2. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{1}\right]$
  3. $\left[\mathrm{M}^{0} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right]$
  4. $\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$

Solution

In $\mathrm{S}=\mathrm{A}(\mathrm{t}+\mathrm{B})+\mathrm{Ct}^{2} ; \mathrm{B}$ is added to time $\mathrm{t}$.
Therefore, dimensions of $\mathrm{B}$ are those of time. ^

Asked in: JEE Mains - Units and Dimensions - Test 3

Practice more Units and Dimensions questions on Aicharya