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

14 rpm

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10 rpm

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2.25 rpm

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7 rpm

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Solution

The correct option is D
7 rpm

Tension in the string $T = m ω^{2} r = 4 π^{2} n^{2} m r$
$∴ T \propto n^{2} \Rightarrow \frac{n_{2}}{n_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow n_{2} = 5 \sqrt{\frac{2 T}{T}} = 7 r p m$

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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

The correct option is D 7 rpm Tension in the string T=mω2r=4π2 n2 mr ∴ T∝n2 ⇒n2n1=√T2T1⇒n2=5√2TT=7 rpm

The correct option is D
7 rpm

Tension in the string $T = m ω^{2} r = 4 π^{2} n^{2} m r$
$∴ T \propto n^{2} \Rightarrow \frac{n_{2}}{n_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \Rightarrow n_{2} = 5 \sqrt{\frac{2 T}{T}} = 7 r p m$