Q. A force $F$ is given by $F = at + bt^{2},$ where $t$ is time. What are the dimensions of $a$ and $b$
A) $MLT^{- 3}$ and $ML^{2}T^{- 4}$
B) $MLT^{- 3}$ and $MLT^{- 4}$
C) $MLT^{- 1}$ and $MLT^{0}$
D) $MLT^{- 4}$ and $MLT^{1}$
Explanation
From the principle of dimensional homogeneity $\lbrack a\rbrack = \left\lbrack \frac{F}{t} \right\rbrack = \left\lbrack MLT^{- 3} \right\rbrack\$ and $\lbrack b\rbrack = \left\lbrack \frac{F}{t^{2}} \right\rbrack = \lbrack MLT^{- 4}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.