The maximum speed of the ball is 15.8 m/s
Given the data in the question;
Mass of the ball; [tex]m = 2kg\\[/tex]
Radius of the circle(rope length); [tex]r = 10m[/tex]
Maximum tension allowed in the string; [tex]T_{max} = 50N[/tex]
We know that the centripetal force for the circular motion of the ball is provided by the tension in the string.
Hence, Maximum Tension [tex]T_{max}[/tex] = Centripetal Force
Now, the formula for Centripetal Force [tex]F_c = \frac{mv^2}{r}[/tex]
where m is the mass, v is the velocity and r is the radius.
Since Maximum Tension [tex]T_{max}[/tex] = Centripetal Force
Maximum Tension [tex]T_{max} = \frac{mv^2}{r}[/tex]
Since we are looking for speed, we make 'v' the subject of the formula
[tex]v = \sqrt{\frac{T_{max}\ *\ r}{m} }[/tex]
[tex]We\ know\ that\ a\ Newton\ (N) = 1 kg.m/s^2[/tex]
Now, we substitute in our given values
[tex]v = \sqrt{\frac{50kg.m/s^2\ *\ 10m}{2kg} }[/tex]
[tex]v = \sqrt{250m^2/s^2}[/tex]
[tex]v = 15.8 m/s[/tex]
Therefore, the maximum speed of the ball is 15.8 m/s
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