The velocity of a paritcle (v) at an instant t is given by `v=at+bt^(2)`. The dimesion of b is

Options

A. [L]
B. `[LT^(-1)]`
C. `[LT^(-2)]`
D. `[LT^(-3)]`

Answer

C

Explanation

Given ` v = at + bt ^ 2 `
Applying the law of homogeneity
` [v] = [bt^ 2 ] `
` [Lt^( - 2) ] = [bt^( -2) ] rArr [b] = [Lt^( -3)] `