# Maximum Speed in Uniform Circular Motion Given: - Mass, \( m = 2\,\mathrm{kg} \) - Radius, \( r = .6\,\mathrm{m} \) - Maximum tension (centripetal force), \( T_{\text{max}} = 100\,\mathrm{N} \) ## Formula The maximum tension provides the maximum centripetal force: \[ T_{\text{max}} = F_c = \frac{mv^2}{r} \] ## Solve for Maximum Speed (\(v_{\text{max}}\)) \[ T_{\text{max}} = \frac{mv^2}{r} \] \[ v^2 = \frac{T_{\text{max}} \cdot r}{m} \] \[ v = \sqrt{\frac{T_{\text{max}} \cdot r}{m}} \] Plug in the values: \[ v = \sqrt{\frac{100 \times .6}{2}} \] \[ v = \sqrt{\frac{60}{2}} \] \[ v = \sqrt{30} \] \[ v \approx 5.48\,\mathrm{m/s} \] ## Closest Option - **5.2 m/s** ## Final Answer **The maximum speed the object can be rotated is \(\boxed{5.2\,\mathrm{m/s}}\).**