Question

The velocity v of a particle depends upon the time t according to the equation $v=a+bt+\frac{c}{d+t}$.The dimensions of a, b, c and d are

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

Answer 1

The correct option is A $\left[L{T}^{-1}\right],\left[L{T}^{-2}\right],\left[L\right],\left[T\right]$

From principle of homogeneity [a] = [v]
Or $\left[a\right]=\left[L{T}^{-1}\right)]$
$\left[bt\right]=\left[v\right]$
Or $\left[bT\right]=\left[L{T}^{-1}\right]$
Or $\left[b\right]=\left[L{T}^{-2}\right]$
Or $\left[d\right]=\left[T\right]$
$\left[\frac{c}{d+t}\right]=\left[v\right]$
$\left[c\right]=\left[c\right][d+t]=\left[L{T}^{-1}\right]\left[T\right]$
$\left[c\right]=\left[L\right]$