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