The force F = A cos Bx + C sin Dt where x is the displacement and t is time. Find the dimensions of A/C.
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Trigonometric functions are dimensionless quantities.
By dimensional analysis,
dimension of F = dimension of A = dimension of C = [MLT⁻²]
Dimension of A/C = [MLT⁻²]/[MLT⁻²] = [M⁰L⁰T⁰]
By dimensional analysis,
dimension of F = dimension of A = dimension of C = [MLT⁻²]
Dimension of A/C = [MLT⁻²]/[MLT⁻²] = [M⁰L⁰T⁰]
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