Part a)
Centripetal acceleration is defined as
[tex]a_c = \frac{v^2}{R}[/tex]
now here we know that
[tex]v = 3m/s[/tex]
[tex]R = 2 m[/tex]
m = 3 kg
now from above formula we have
[tex]a_c = \frac{3^2}{2}[/tex]
[tex]a_c = 4.5 m/s^2[/tex]
Part b)
Maximum possible tension in the string is given as
[tex]T = 50 N[/tex]
now by force equation we have
[tex]F = ma[/tex]
[tex]50 = 3 a[/tex]
[tex]a = \frac{50}{3} m/s^2[/tex]
now again by above formula
[tex]\frac{v^2}{R} = \frac{50}{3}[/tex]
[tex]v = \sqrt{\frac{50 \times 2}{3}}[/tex]
[tex]v = 5.77 m/s[/tex]
a) a=v^2/R=4.5 m/s/s
b) F=ma=mv^2/R, so
[tex]v=\sqrt{FR/m}=5.77[/tex] m/s
