Question

# A force $$\displaystyle F$$ is given by $$F = at + bt^2$$, where $$t$$ is time. The dimensions of $$a$$ and $$b$$ are :

A
[MLT3] and [MLT4]
B
[MLT4] and [MLT3]
C
[MLT1] and [MLT2]
D
[MLT2] and [MLT0]

Solution

## The correct option is C $$[M\,L\,T^{-3}]$$ and $$[M\,L\,T^{-4}]$$Dimensions of force are $$MLT^{-2}$$. Thus, both $$at$$ and $$bt^2$$ must have units of force.Thus, $$|a|T=MLT^{-2}$$ or $$|a|=MLT^{-3}$$Also, $$|b|T^2=MLT^{-2}$$ or $$|b|=MLT^{-4}$$Physics

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