Question

the velocity v of a particle at time t is given by the following relation where a,b and c are constants . find the dimensions of a,b and c (v=at+b/t+c)

Answer 1

Answer:

Dimensions of velocity are [LT⁻¹]. The dimensions of c must be the same as that of velocity, i.e. [LT⁻¹]. ... Hence, the dimensions of a would be [LT⁻²] and that of b would be [LT⁰].

Answer 2

Answer:

Explanation:

v=at+b/t+c

We know that, Two entities can only be added if their dimensions are same,

so Dimensions of [at] = Dimensions of [b/t] = Dimensions of [c] = Dimensions of [v]

=> [aT] = [v] = [LT⁻¹]=> [a] = [LT⁻²] ,   Dimensions of [a]

=>[bT⁻¹] = [LT⁻¹]=> [b] = [L], Dimensions of [b]

=> [c] = [LT⁻¹] , Dimensions of [c]