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SHM expression

A force F i...

Question

A force $F$ is given by $F = a t + b t^{2}$ , where $t$ is time. The dimensions of $a$ and $b$ are :

[M L T^{- 3}]

and

[M L T^{- 4}]

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[M L T^{- 4}]

and

[M L T^{- 3}]

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[M L T^{- 1}]

and

[M L T^{- 2}]

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[M L T^{- 2}]

and

[M L T^{0}]

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Solution

The correct option is C $[M L T^{- 3}]$ and $[M L T^{- 4}]$
Dimensions of force are $M L T^{- 2}$ . Thus, both $a t$ and $b t^{2}$ must have units of force.
Thus, $| a | T = M L T^{- 2}$ or $| a | = M L T^{- 3}$
Also, $| b | T^{2} = M L T^{- 2}$ or $| b | = M L T^{- 4}$

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[M L T^{- 1}]

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