The velocity v of a particle at a time t is given by v=at+b/t+c. Where a,b,c are constants . What are the dimensions of a,b & c ?
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408
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]
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]
Answered by
117
Dimensions of velocity are [LT⁻¹]. The dimensions of c must be the same as that of velocity, i.e. [LT⁻¹]. The dimensions of at and b/t must also be the same as that of velocity. Hence, the dimensions of a would be [LT⁻²] and that of b would be [LT⁰].
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