Question

The velocity v of a point at time t is given by $v=at+\frac{b}{t+c}$. The dimension of a, b and c are respectively:

• A. $L{T}^{-1}{L}^{-1}$ and $T$
• B. $L{T}^2,L$ and $T$
• C. $L{T}^{-2},L$ and $T$
• D. $L,LT$ and $T^2$

Answer 1

Answer: (C)

$L{T}^{-2},L$ and $T$

Given , $v=at+\frac{b}{t+c}$
$L{T}^{-1}=\left[a\right]T+\frac{\left[b\right]}{T+\left[c\right]}$
Both side dimension should be same.

So, $\left[a\right]=L{T}^{-2},\left[b\right]=L,\left[c\right]=T$