Question

On horizontal smooth surface a mass of $2kg$ is whirled in a horizontal circle by means of a string at an initial angular speed of $5rpm$. Keeping the radius constant the tension in the string is doubled. The new angular speed is near by

• A. 14 rpm
• B. 10 rpm
• C. 2.25 rpm
• D. 7 rpm

Answer 1

The correct option is D 7 rpm

$T=m{\omega }^{2}r=2\times (2\pi \times 5{)}^2\times r)=2\times 4{\pi }^2\times 25r2T=2\times (2\pi \times n^{\prime })r2T=2\times 4{\pi }^2{n}^{\prime 2}\times \frac{T}{2\times 4{\pi }^2\times 25}{n}^{\prime 2}=50n^{\prime }=7rpm$