Q. If $F$ denotes force and $t$ time, then in equation $F = at^{- 1} + \ bt^{2},$ the dimensions of $a$ and $b$ respectively are
A) $\left\lbrack {LT}^{- 4} \right\rbrack\ and\ \left\lbrack {LT}^{- 1} \right\rbrack$
B) $\left\lbrack {LT}^{- 1} \right\rbrack\ and\ \left\lbrack {LT}^{- 4} \right\rbrack$
C) $\left\lbrack {MLT}^{- 4} \right\rbrack\ and\ \left\lbrack {MLT}^{- 1} \right\rbrack$
D) $\left\lbrack {MLT}^{- 1} \right\rbrack\ and\ \left\lbrack {MLT}^{- 4} \right\rbrack$
Explanation
By the principle of dimensions homogeneity $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F = at^{- 1}$ $\ \ \ \ \ \ \ \left\lbrack {MLT}^{- 2} \right\rbrack = \ a\left\lbrack T^{- 1} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a = \left\lbrack {MLT}^{- 1} \right\rbrack\$ Similarly for $b = \left\lbrack {MLT}^{- 4} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.