Question

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

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

Answer 1

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

Two terms can be added or subtracted if their dimensions are same.

Thus $c$ has the dimension of time i.e. $\left[T\right]$

Dimension of $v$ and $at$ must be same.

Thus dimensions of $\left[a\right]=\frac{\left[v\right]}{\left[t\right]}=\frac{\left[L{T}^{-1}\right]}{\left[T\right]}=\left[L{T}^{-2}\right]$

Dimensions $\left[b\right]=\left[v\right]\left[t\right]=\left[L{T}^{-1}\right]\left[T\right]=L$