Question

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

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

Answer 1

The correct option is A $L{T}^{-2},L$ and $T$

According to the principle of dimensional homogenity
Dimension of $v=$ dimension of $at$ = dimension of $\frac{b}{t+c}$
Dimension of $a=\frac{\left[v\right]}{\left[t\right]}=\frac{L{T}^{-1}}{T}=\left[L{T}^{-2}\right]$
Dimension of $b=\left[v\right]\left[t\right]=\left[L{T}^{-1}T\right]=\left[L\right]$
Dimension of $c=\left[t\right]=\left[T\right]$