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A force is given by F = at + bt², where t is time. What are the dimensions of constants a and b respectively?

1. [MLT⁻⁴], [MLT⁻²]
2. [MLT⁻³], [MLT⁻⁴]
3. [ML²T⁻³], [ML²T⁻²]
4. [ML²T⁻³], [ML³T⁻⁴]

Correct answer: [MLT⁻³], [MLT⁻⁴]

Solution

Since F = at, the dimension of a = [F/t] = MLT⁻³; since F = bt², the dimension of b = [F/t²] = MLT⁻⁴.

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