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The velocity of a particle v at an insta...

The velocity of a particle v at an instant t is given by `v = a t + b t^(2)`. Th e dimensions of b is

A

[L]

B

`[LT^(-1)]`

C

`[LT^(-2)]`

D

`[LT^(-3)]`

Text Solution

Verified by Experts

The correct Answer is:
D
By the principle of homogeneity, `a//V^(2)` is of the dimensions of pressure  and b is of the dimensions of volume.
[a] = [pressure] `[V^(2)]= [ML^(-1) T^(-2)] [L^(6)]= [ML^(5)T^(-2)]`
[b] `=[V]= L^(3)`
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