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 the tension in the string is doubled. The new speed is nearly ....... $rpm$
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(d) Tension in the string $T = m{\omega ^2}r = 4{\pi ^2}{n^2}mr$
$T \propto {n^2}$
$T \propto {n^2}$
$⇒$ $\frac{{{n_2}}}{{{n_1}}} = \sqrt {\frac{{{T_2}}}{{{T_1}}}} $
$⇒$ ${n_2} = 5\sqrt {\frac{{2T}}{T}} = 7\,rpm$
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