Question

If $v=\frac{A}{t}+Bt^{2}+Ct^{3}$ where $v$ is velocity, $t$ is time and $A, \, B$ and $C$ are constants, then the dimensional formula of $B$ is

• A. $\left[\right.M^{0}LT^{0}\left]\right.$
• B. $\left[\right.ML^{0}T^{0}\left]\right.$
• C. $\left[\right.M^{0}L^{0}T^{ \, }\left]\right.$
• D. $\left[\right.M^{0}LT^{- 3}\left]\right.$

Answer 1

Answer: (D)

$As , v =\frac{ A }{ t }+ Bt ^{2}+ Ct ^{3}$
So, we can write the dimensional equation as:
$[v]=\left[B t^2\right]$
$\therefore[B]=\frac{[v]}{\left[t^2\right]}=\frac{\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^{-1}\right]}{\left[\mathrm{T}^2\right]}=\left[\mathrm{L}^1 \mathrm{~T}^{-3}\right]$