Question

The velocity of a body moving viscous medium is given by $V=\frac{A}{B}[1-e^{-t/B}]$ where $t$ is time, $A$ and $B$ are constants. Then the dimensional formula of $A$ is:

• A. $M^0{L}^0{T}^0$
• B. $M^0{L}^1{T}^0$
• C. $M^0{L}^1{T}^{-1}$
• D. $M^1{L}^1{T}^{-1}$

Answer 1

The correct option is B $M^0{L}^1{T}^0$

In $e^{\frac{-t}{B}}$ is the exponential term. So, the $\frac{t}{B}$ is constant.

So, B has the dimensions as:

$B=\left[T\right]$

On the other hand, the dimension of $\frac{A}{B}$ will be the same as that of the velocity.

$\frac{A}{B}$ has dimensions as velocity

$\left[L{T}^{-1}\right]=\frac{a}{\left[T\right]}$

dimensional formula of A is $M^0{L}^1{T}^0$