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The velocity v of a particle is given in...

The velocity `v` of a particle is given in terms of time `t` by the equation
`v=at+(b)/(t+c)` The dimensions of `a,b` and `c` are :

A

`L,LT` and `T^(2)`

B

`LT^(-2),L` and `T`

C

`L^(2),T` and `LT^(2)`

D

`LT^(2)LT` and `L`

Text Solution

Verified by Experts

The correct Answer is:
B
`v=at+(b)/(t+c),` at has same dimensions as `v`
`:.at=LT^(-1)` or `a=LT^(-2)`
`c` has the same dimensions as `t. :.c=T`
Also `(b)/(t+c)`has the dimensionsof `v`
`:.b=vt=LT^(-1).T^(1)=L`
Thus `a,b,c` respectively are `LT^(2),L,T.`
Hence correct choice is `(b)`.
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