Question #cb7bf

2 Answers

a -> [L/(T*T)]a[LTT]

b -> [L/T]b[LT]

c -> [T]c[T]

Explanation:

I am considering the equation as :

v = at + b * t/(t+c)v=at+btt+c

Let me know if this is not what you meant.

In any equation, each term separated by ++ or - must have same dimension or else cannot be added.

So here vv , a*tat , and b * t/(t+c)btt+c must have same dimension. Since we know the dimension of velocity as [L/T][LT], the other 2 terms should also have the same dimension.

So a*tat has dimension [L/T][LT]

[aT] = [L/T][aT]=[LT]

[a] = [L/(T*T)][a]=[LTT]

Similarly, let us consider the denominator part of 2nd term. (t + c)(t+c). Here tt and cc must have the same dimensions since they are being added, so

[c] = [T][c]=[T]

The rest

[b T/(c+T)] = [L/T][bTc+T]=[LT]

[bT/T] = [L/T][bTT]=[LT], since cc and TT are being added

[b] = [L/T][b]=[LT]

Hope you have a good day.

Mar 30, 2017

The dimension of aa and bb is =[L][T]^-1=[L][T]1
The dimension of cc is [T][T]

Explanation:

The dimension of cc is [T][T]

The dimension of vv is [L][T]^-1[L][T]1

The dimension of atat is [L][L]

The dimension of aa is [L][T]^-1[L][T]1

The dimension of bb is [L][T]^-1[L][T]1

I considered the equation as

v=((at+bt))/((t+c))v=(at+bt)(t+c)

LHSLHS is =[L][T]^-1=[L][T]1

RHSRHS is =([L][T]^-1)/[T]*[T]=[L][T]1T[T]

Therefore,

aa is [L][T]^-1[L][T]1