18. a. Derive an expression for time period of a simple pendulum using dimensional analysis. b. A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kg m2 s-2. Suppose we

employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time

is γ s. Show that a calorie has a magnitude of 4.2 α-1 β-2 γ2 in terms of the new units

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