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Dimensional Analysis

A force F i...

Question

A force $F$ is given as $F = a t + b t^{2}$ , where t is time. What are the dimensions of a and b?

[M L T^{- 1}]

and

[M L T^{0}]

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[M L T^{- 3}]

and

[M L^{2} T^{4}]

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[M L T^{- 4}]

and

[M L T^{1}]

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[M L T^{- 3}]

and

[M L T^{- 4}]

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Solution

The correct option is D $[M L T^{- 3}]$ and $[M L T^{- 4}]$
Dimensions for force is $[M L T^{- 2}]$ .
Thus $[M L T^{- 2}] = [a] [T]$ and $[M L T^{- 2}] = [b] [T^{2}]$
$⟹ [a] = [M L T^{- 3}]$ and $[b] = [M L T^{- 4}]$

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The dimensions of k in the equation F = - k x (where F is force and x is displacement)

[M L T^{- 1}]

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