Q. If $v = \frac{A}{t} + Bt^{2} + Ct^{3}$ where $v$ is velocity, $t$ is time and $A,B$ and $C$ are constants, then the dimensional formula of $B$ is
A) $\lbrack M^{0}LT^{0}\rbrack$
B) $\lbrack ML^{0}T^{0}\rbrack$
C) $\lbrack M^{0}L^{0}T^{\ }\rbrack$
D) $\lbrack M^{0}LT^{- 3}\rbrack$
Explanation
Velocity $v = Bt^{2}$ $\therefore\ B = \frac{v}{t^{2}} = \frac{\lbrack LT^{- 1}\rbrack}{\lbrack T^{2}\rbrack} = \lbrack LT^{- 3}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.