A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The

Question

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?

Accepted Answer

1. **Identify the Force:** For a body moving in a horizontal circle attached to a string, the centripetal force required to maintain the circular path is provided by the tension ($T$) in the string [Source 62, 68].
2. **Formula:** The centripetal force is given by $F_c = \frac{mv^2}{r}$. Thus, $T = \frac{mv^2}{r}$.
3. **Condition for Breaking:** The string breaks if the tension exceeds the maximum tension ($T_{max}$). To find the maximum speed ($v_{max}$), we equate the tension to the breaking limit.
   $$ T_{max} = \frac{m v_{max}^2}{r} $$
4. **Calculation:**
   - Mass ($m$) = 0.25 kg
   - Radius ($r$) = Length of string = 1.96 m
   - Max Tension ($T_{max}$) = 25 N
   $$ 25 = \frac{0.25 	imes v_{max}^2}{1.96} $$
   $$ v_{max}^2 = \frac{25 	imes 1.96}{0.25} = 100 	imes 1.96 = 196 $$
   $$ v_{max} = \sqrt{196} = 14 	ext{ m/s} $$

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