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Answer:
1. The centripetal acceleration
[tex] a_c \approx \boxed {110.28 \, \text{m/s}^2}[/tex]
2. The force exerted on the string
[tex]F \approx \boxed {27.57 \, \: {N}}[/tex]
• Mass of the ball,
[tex]m = 0.25 \, \: {kg}[/tex]
• Radius of the circle,
[tex]r = 0.70 \, \: {m}[/tex]
• Revolutions per second,
[tex]f = 2.0 \, \: {rps}[/tex]
[tex]f = 2.0 \, \: {rps}[/tex]
[tex]\omega = 2\pi \times 2.0 = 4\pi \, \text{rad/s}[/tex]
The centripetal acceleration ( a_c ) is given by:
[tex]a_c = \omega^2 r[/tex]
[tex] \omega = 4\pi[/tex]
[tex]r = 0.70 \, \: {m}[/tex]
[tex]a_c = (4\pi)^2 \times 0.70[/tex]
[tex]a_c = 16\pi^2 \times 0.70[/tex]
[tex]a_c \approx 16 \times 9.87 \times 0.70[/tex]
[tex]a_c \approx 110.28 \, \: {m/s}^2 [/tex]
The force exerted on the string is the centripetal force, which can be calculated using:
[tex]F = m a_c[/tex]
[tex]m = 0.25 \, \text{kg}[/tex]
[tex] a_c = 110.28 \, \: {m/s}^2 \):[/tex]
[tex]F = 0.25 \times 110.28[/tex]
[tex]F \approx \boxed{ 27.57 \, \text{N}}[/tex]