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Question

Find the value of the period (i.e., time required for one cycle) if the second hand on a watch rotates 60 cycles per hour. Also find the relationship (i) between frequency and period (ii) between their units.

Moderate

Solution

Frequency

,$\begin{array}{l}v=\frac{60\text{cycles}}{\text{hour}}=\frac{60}{h}\times \frac{1h}{60\mathrm{min}}\\ =1{\mathrm{min}}^{-}[\because 1h=60\mathrm{min}]\end{array}$

Period, $T=\frac{1}{v}=\frac{1}{1{\mathrm{min}}^{-1}\u200a}=1\mathrm{min}$

Since T and u are reciprocal of each other, their units will be, for example, s and ${\mathrm{s}}^{-}(=\mathrm{Hz})$ respectively.

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