Q. In a system of units if force $(F)$, acceleration $(A)$, and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
A) $FA^{2}T$
B) $FAT^{2}$
C) $F^{2}AT$
D) $FAT$
Explanation
$E = KF^{a}A^{b}T^{c}$ $\left\lbrack ML^{2}T^{- 2} \right\rbrack = \left\lbrack MLT^{- 2} \right\rbrack^{a}\left\lbrack LT^{- 2} \right\rbrack^{b}\lbrack T\rbrack^{c}$ $\left\lbrack ML^{2}T^{- 2} \right\rbrack = \lbrack M^{a}L^{a + b}T^{- 2a - 2b + c}\rbrack$ $\therefore a = 1,\ a + b = 2\ \Rightarrow b = 1$ And $- 2a - 2b + c = - 2 \Rightarrow c = 2$ $\therefore E = KFAT^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.