Question

The velocity of a body is given by the equation $v=\frac{b}{t}+c{t}^2+d{t}^3$ The dimensional formula of $b$ is

• A. $\left[M^{0}L{T}^0\right]$
• B. $\left[M^0{L}^0{T}^0\right]$
• C. $\left[M{L}^0{T}^0\right]$
• D. $\left[ML{T}^{-1}\right]$

Answer 1

The correct option is A $\left[M^{0}L{T}^0\right]$

$LHS$ has the dimension $\left[L^1{T}^{-1}\right]$ From the principle of homogeneity each term in $RHS$ should have the dimension of velocity.
$\left[\frac{d}{t}\right]=\left[v\right]\text{or}\left[b\right]=\left[vt\right]\left[b\right]=\left[L^1{T}^{(-1)}\right]\left[T^1\right]\left[b\right]=\left[L\right]$