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Q.

A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936/x ms^-2 . The value of x is _______. (Take $π$ = 22/7)

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answer is 125.

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Detailed Solution

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$\begin{array}{l} a = {rω}^{2} \Rightarrow a = 180 \times 10^{- 2} \times {(\frac{28 \times 2 π}{60})}^{2} \\ a = 1.8 \times \frac{28}{60} \times \frac{28}{60} \times 4 \times \frac{22}{7} \times \frac{22}{7} \\ = \frac{1.8 \times 4 \times 4 \times 4 \times 22 \times 22}{60 \times 60} = \frac{1936}{x} \end{array}$

$x = \frac{1936 \times 60 \times 60}{1.8 \times 4 \times 4 \times 4 \times 22 \times 22} = 125$

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