Question

in the equation v = at + b / ( t^2+ c ) , write the dimensions of a, b, c [v = velocity, t = time]​

Answer 1

Explanation:

In the equation v=at+bt², what is the dimension of b?

let us assume v represents velocity and t represents time in given expression then we may find dimensions of a & b as following

L.H.S=v

=[L][T^(-1)]

R.H.S=at+bt^2

[at]=[bt^2](since only quantity of same dimensions are additive.)

[bt^2]=[bT^2]

since LHS should be equal to RHS

so

[bT^2]=[LT^(-1)]

b=LT^(-3)

so dimension of b will be [LT^(-3)]