The body is accelerating upward toward the center of the circle it traces out with magnitude
a = v ² / R
where
v = linear speed of the body
R = 3.4 m = radius of the circle it traces/length of the string
The only forces acting on it at the lowest point are the tension T of the string pulling upward on the body and weight W = mg of the body pulling it downward. By Newton's second law, we have
∑ F = T - mg = ma
Replace the acceleration with the expression from earlier and solve for v :
300 N - (17 kg) g = (17 kg) v ² / (3.4 m)
v ² = ((3.4 m) 300 N - (17 kg) g) / (17 kg)
v = √[ ((3.4 m) 300 N - (17 kg) g) / (17 kg) ]
v ≈ 5.16527 m/s ≈ 5.2 m/s
