The velocity `upsilon` of a particle depends upon time t, according to the equation `upsilon = a+ bt +(c )/(d +t)` Write the dimensions of a,b,c, and d.

Options

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

Answer

A

Explanation

From principle of homogeneity `[a]=[v]or=[LT^(-1)]`
`[bt]=[v]`
or `[b]=([v])/([t])=([LT^(-1)])/([T])`or`[b]=[LT^(-2)]`
Similarly,`[d]=[t]=[T]`
Further, `([c])/([d+t])=[v]or[c]=[v][d+t]`
or `[c]=[LT^(-1)][T] or [c]=[L]`
`:.` Dimensions of `a=[LT^(-1)]`
Dimensions of `b=[LT^(-2)]`
Dimensions of `c=[L]`
Dimensions of `d=[T]`