Single Choice

If the force is given by $$ F$$ = $$at+bt^2$$ with $$ t $$ as time. The dimensions of a and b are:

A$$[MLT^{-4}], [MLT^{-2}]$$
B$$[MLT^{-3}], [MLT^{-4}]$$
Correct Answer
C$$[ML^2T^{-3}], [ML^2T^{-2}]$$
D$$[ML^2T^{-3}], [ML^3T^{-4}]$$

Solution

Dimension of force F : $$[MLT^{-2}]$$
$$F=at+bt^2$$
$$\implies $$ Dimension of $$a:[MLT^{-2}]\times [T^{-1}]$$=[MLT^{-3}]$$
Dimensions of $$b:[MLT^{-2}]\times [T^{-2}]$$=[MLT^{-4}]$$

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