The velocity v of a particle at time t is given by `v=at+b/(t+c)`, where a, b and c are constants. The dimensions of a, b, c are respectively :-

Options

A. `{:(a,b,c),("[L],[LT],[T^(2)]):}`
B. `{:(a,b,c),("[L^(2)],[T],[LT^(-2)]):}`
C. `{:(a,b,c),("[LT^(2)],[LT],[L]):}`
D. `{:(a,b,c),("[LT^(2)],[L],[T]):}`

Answer

D

Explanation

Given `v=at +(b)/(t+c)`
Since, LHS is equal the velocity, so at and `(b)/(t+c)` must have the dimensions of velocity.
`:. At = or a=(v)/(t)`
`rArr ([LT^(-1)])/([T])=[LT^(-2)]`
Now, C= times ( `:.` quanities are added )
`:. C=t=[T]`
Now, `(b)/(t+c)=v`
`:. b=vxx "time"=[LT^(-1)][T]=[L]`