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  4. 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) m s-2. The value of x ( Take π=(22/7) )

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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 $\frac{1936}{x} m s^{-2}$. The value of $x$ _____
( Take $\pi=\frac{22}{7}$ )

JEE MainJEE Main 2023Motion in a Plane

Solution:

$a=\omega^2 R =\left(\frac{28 \times 2 \pi}{60}\right)^2 \times 1.8 $
$ =\left(\frac{56}{60} \times \frac{22}{7}\right)^2 \times 1.8 $
$ =\frac{(44)^2}{225} \times 1.8 $
$ =\frac{1936 \times 1.8}{225}$
$ x=125$