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 $\frac{1936}{X} {ms}^{- 2} .$ The value of X------------ $(Take π = \frac{22}{7})$

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answer is 125.

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Detailed Solution

$a = r ω^{2} \Rightarrow a = 180 \times 10^{- 2} \times {(\frac{28 \times 2 π}{60})}^{2}$

$a = 1.8 \times \frac{28}{60} \times \frac{28}{60} \times 4 \times \frac{22}{7} \times \frac{22}{7}$

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

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

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