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  4. A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant, if we want the tension in the string to be doubled, then the new speed should nearly be

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Q. A mass of $2 \, kg$ is whirled in a horizontal circle by means of a string at an initial speed of $5$ revolutions per minute. Keeping the radius constant, if we want the tension in the string to be doubled, then the new speed should nearly be

NTA AbhyasNTA Abhyas 2022

Solution:

$F = m \omega^{2} r$
$= mr (2 n \pi)^{2}$
thus $F \times n ^{2} n =$ resolution per second.
thus $\frac{2 F}{F}=\frac{ n ^{\prime 2}}{ n }$
or $n ^{\prime}=\sqrt{2} n$
$=5 \sqrt{2} \,rpm$
$=7\, rpm$