Question

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

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

Answer 1

Answer: (A)

In the equation, left hand side has the dimension of velocity. Then from the principle of homogeneity each term in the right-hand side should have the dimensions of velocity $\left[\frac{b}{t}\right]=\left[v\right]$ or $\left[b\right]=\left[vt\right]=\left[L\right]$