Question

The velocity of a moving particle depends upon time t as $v=at+\frac{b}{t+c}$. Then dimensional formula for b is?

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^0{L}^1{T}^0\right]$
• C. $\left[M^0{L}^1{T}^{-1}\right]$
• D. $\left[M^0{L}^1{T}^{-2}\right]$

Answer 1

Answer: (B)

$\left[M^0{L}^1{T}^0\right]$

We have, $v=at+\frac{b}{(t+c)}$

Here, c is added by t , therefore, $c=\left[T\right]$

Again $at=L{T}^{-1}$

Therefore, $a$ =$\frac{L{T}^{-1}}{T}$ =$L{T}^{-2}$

And $\frac{b}{T}=L{T}^{-1}$

Therefore, $\left[b\right]$ = $\left[L\right]$