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  4. The velocity of a particle (v) at an instant t is given by v = at + bt2. The dimension of b is

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

WBJEEWBJEE 2008Physical World, Units and Measurements

Solution:

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