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A force F is given by F = at + bt^(2) , ...

A force `F` is given by `F = at + bt^(2)` , where `t` is time . What are the dimensions of `a and b`?

A

`[MLT^(-4)] and [MLT]`

B

`[MLT^(-1)] and [MLT^(0)]`

C

`[MLT^(-3)] and [MLT^(-4)]`

D

`[MLT^(-3)] and [MLT^(0)]`

Text Solution

Verified by Experts

The correct Answer is:
C
By principle of homogeneity, dimensiosns of each term must be same, i.e `[F] = [a t] = [b t^(2)]`
So, `[a]=[(F)/(t)]=(MLT^(-2))/(T)=MLT^(-3)`
`[b]=[(F)/(t^(2))] = (MLT^(-2))/(T^(2))=MLT^(-4)`
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