## Yes, your answers are correct.

To find the velocity of the swinging ball, you used the formula v = rw. In this formula, r is the length of the chain (1.25 m) and w represents the angular velocity (2.0 s^-1). By plugging in these values, you correctly calculated the velocity of the ball to be 2.5 m/s.

To find the kinetic energy of the ball, you used the formula KE = (1/2)mv^2. Here, m is the mass of the ball (5.00 kg) and v is the velocity of the ball (2.5 m/s). By substituting these values, you correctly determined the kinetic energy to be 31.25 J.

To find the inertia of the ball, you used the formula I = mr^2. In this formula, m represents the mass of the ball (5.00 kg) and r represents the length of the chain (1.25 m). By plugging in these values, you correctly found the inertia of the ball to be 15.6 kg*m^2.

To find the kinetic energy using inertia, you used the formula KE = 0.5Iw^2. In this formula, I represents the inertia of the ball (15.6 kg*m^2) and w represents the angular velocity (2.0 s^-1). By substituting these values, you correctly calculated the kinetic energy to be 15.6 J.

To find the centripetal force acting on the ball, you used the formula Fc = (mv^2)/r. Here, m represents the mass of the ball (5.00 kg), v represents the velocity of the ball (2.5 m/s), and r represents the length of the chain (1.25 m). By substituting these values, you correctly determined the centripetal force to be 25 N.

Well done!