Q. The velocity of a particle $v$ at an instant $t$ is given by $v = at + bt^{2}$ the dimension of $b$ is
A) $\lbrack L\rbrack$
B) $\left\lbrack {LT}^{- 1} \right\rbrack$
C) $\left\lbrack {LT}^{- 2} \right\rbrack$
D) $\left\lbrack {LT}^{- 3} \right\rbrack$
Explanation
Given, $v = at + bt^{2}$ Applying the law of homogeneity $\lbrack v\rbrack = \left\lbrack bt^{2} \right\rbrack$ Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\lbrack LT^{- 1} \right\rbrack = \left\lbrack bT^{2} \right\rbrack$ Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack b\rbrack = \left\lbrack LT^{- 3} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.