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

B

`LT^(2),LT,L`

C

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

D

`L,LT,T^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`v=at+(b)/(t+c)`
By principle of homogeneity,
dim `(at)`=dim`(v)`implies`a=(LT^(-1))/(T)=[LT^(-2)]`
Also dim `(c )`=dim`(t)`=`[T]`
Now `(b)/("time")=Velocity:.b=velocityxxtime`
` =LT^(-1)xxT=[L]`
So correct choice is `(c ).`
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