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Question

What are the dimensions of a and b in the relation F=ax+bt2 where F is force, x is distance and t is time?

A
[ML12T2], [MLT4]
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B
[ML32T2], [MLT2]
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C
[M2L12T12], [M3L12T2]
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D
[M3L12T2], [ML32T2]
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Solution

The correct option is A [ML12T2], [MLT4]
Applying principle of homogeneity, every term in an algebraic equation of physical quantities must have the same unit.

Thus, each term in the equation must have the dimensions of force.

[MLT2]=[a][L1/2]=[b][T2]

[a]=[ML1/2T2]
[b]=[MLT4]

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