Question

Velocity of particle is given as $v=A{e}^{\frac{At}{B}}$. Find the dimensions of B.

• A. [M]
• B. [L]
• C. $\left[L{T}^{-1}\right]$
• D. $\left[L{T}^{-2}\right]$

Answer 1

The correct option is B [L]

$v=A{e}^{A\frac{t}{B}}$
$\left[v\right]=\left[A\right]=\left[L{T}^{-1}\right]$
$\left[\frac{At}{B}\right]=M^0{L}^0{T}^0$
$B=\frac{At}{M^0{L}^0{T}^0}=\frac{L{T}^{-1}.T}{M^0{L}^0{T}^0}=\left[L\right]$