Question

The velocity $v$ of a particle at time $t$ is given by $v=at+\frac{b}{t+c}$ The dimensions of $a,b,c$ are respectively

• A. $\left[L{T}^{-2}\right],\left[L\right],\left[T\right]$
• B. $\left[L^2\right],\left[T\right]$ and $\left[L{T}^2\right]$
• C. $\left[L{T}^2\right],\left[LT\right]$ and [L]
• D. $\left[L\right],\left[LT\right]$ and $\left[T^2\right]$

Answer 1

Answer: (A)

$\left[L{T}^{-2}\right],\left[L\right],\left[T\right]$

As c is added to t, $\therefore \left[c\right]=\left[T\right]$

Applying principle of homogeneity, $\left[a\right]=\left[\frac{v}{t}\right]=\frac{L{T}^{-1}}{T}=\left[L{T}^{-2}\right]$

and $\left[b\right]=\left[v\right(t+c\left)\right]=[L{T}^{-1}\times T]=\left[L\right]$