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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

`[M^(1)L^(1)T^(3)],[M^(1)L^(1)T^(-4)]`

B

`[M^(2)L^(1)T^(2)],[M^(1)L^(1)T^(-2)]`

C

`[M^(1)L^(-1)T^(-2)],[M^(1)L^(2)T^(-3)]`

D

`[M^(-1)L^(1)T^(-4)],[M^(1)L^(1)T^(-3)]`

Text Solution

Verified by Experts

The correct Answer is:
a
In a dimensional equation, all terms must have the same dimensions. In this case, they should have the dimensions of force.
`[F]=[M^(1)L^(1)T^(-2)]`
(i) `[a]=[(F)/(t)]=[(M^(1)L^(1)T^(-2))/(T^(1))]=[M^(1)L^(1)T^(-3)]`
(ii) `[b]=[(F)/(t^(2))]=[(M^(1)L^(1)T^(-2))/(T^(2))]=[M^(1)L^(1)T^(-4)]`
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