Question

v=at+b/t+c+v° Above equation is dimensionally valid equation. Obtain dimensional formula of a, b and c. Here v is velocity, v° is initial velocity, time is t. ​

Answer 1

Answer:

dim(a) = [L/T^2], dim(b)=[L], dim(c)=[L/T]

Explanation:

[L]=dimension of Length ,

[T]=dimension of  Time

1) We have,

given dimensionally  valid equation.

=> Only Similar dimension elements can added or subtracted .

$v=at+\frac{b}{t}+c+v^o\\ \\=>dim(v)=dim(at)=dim(\frac{b}{t})=dim(c)=dim(v^o)\\ \\=> [L/T]=[aT]=[\frac{b}{T}]=[c]=[v^o]$

2) We got that,

$[{\frac{L}{T}]=[aT] \\ \\=>[a]=[\frac{L}{T^2}]$

and

$[\frac{L}{T}]=[\frac{b}{T}]\\ \\=>[b]=[L]$

and

$[\frac{L}{T}]=[c]\\ \\=>[c] = [\frac{L}{T}]$

Hence, our required dimensions are :

$\boxed{dim(a) = [L/T^2], dim(b)=[L], dim(c)=[L/T]}$

Answer 2

Answer:

a= LT*-2,b=L,c=LT*-1

Explanation:

hope it's helpful