Velocity of a particle at time t is expressed as follows :
`v= alpha t+(beta)/(t +gamma)`
Dimensions of `alpha, beta " and "gamma` are respectively.

Options

A. `LT^(-2) , L , T`
B. `L, T, LT^(-2)`
C. `T,L, LT^(-2)`
D. `LT^(-1), L, T`

Answer

A

Explanation

`V = alpha t + (beta)/(t + gamma)`
`[V] = [alpha t] " " [alpha] = ([V])/([t])`
`[alpha] = ([LT^(-1)])/([T]) = [LT^(-2)]`
`t + gamma` syas that dimension of `gamma`
`[gamma] = [t] " " implies " " [gamma] = [T]`
`[V] = [(beta)/(t + gamma)] " " implies " " [beta] = [V][T]`
`[beta] = [LT^(-1)][T] = [L]`