α = (F / v²) sin(βt) (where v = velocity, F = force, t = time). Find the dimension of α and β respectively.
[M¹L⁻¹T⁰], [M⁻¹L⁻¹T⁰]
[M¹LT⁻²], [M⁻¹L¹T⁰]
[M⁻¹L⁻¹T⁻²], [M¹LT⁻²]
[M¹L⁻¹T⁰], [M⁰L⁰T⁻¹]
α = (F / v²) sin(βt)
sin(βt) is dimensionless
So,
α = [F / v²] = [M¹L¹T⁻²] / [LT⁻¹]² = M¹L⁻¹T⁰
β = 1 / [t] = 1 / [T] = M⁰L⁰T⁻¹
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