Question

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω₀. If the length of the string and angular velocity are doubled, the tension in the string which was initially T₀ is now

• A. T₀
• B. T₀/2
• C. 4T₀
• D. 8T₀

Answer 1

Answer: (D)

8T₀

Answer 2

$T = m\omega^{2}l$

∴ $\frac{T_{2}}{T_{1}} = \left( \frac{\omega_{2}}{\omega_{1}} \right)^{2}\left( \frac{l_{2}}{l_{1}} \right)$⇒ $\frac{T_{2}}{T_{0}} = \left( \frac{2\omega}{\omega} \right)^{2}\left( \frac{2l}{l} \right)$⇒ $T_{2} = 8T_{0}$