Question

The velocity of a particle $(v)$ at an instant $t$ is given by $v=at+b{t}^2$. The dimension of $b$ is

• A. $[L]$
• B. $[L{T}^{-1}]$
• C. $[L{T}^{-2}]$
• D. $[L{T}^{-3}]$

Answer 1

Answer: (D)

Given, that $v=at+b{t}^2$
Applying the law of homogeneity $[v]=\left[b{t}^2\right]$ or
$\left[L{T}^{-1}\right]=\left[b{T}^2\right]\text{ or }[b]=\left[L{T}^{-3}\right]$