The centripetal force is calculated using the mass, the centripetal acceleration, and the radius of the circular path. The provided answers are incorrect; the correct magnitude of the centripetal force for this problem is 0.0079 N, and the direction is towards the center of the circle.
The question is asking to calculate the centripetal force acting on a ball of mass 400g (0.4 kg) that is revolving around a circular path of radius 5cm (0.05 m) with one revolution each 10 seconds. To find the centripetal force Fc, we can use the formula Fc = m * ac, where m is mass and ac is the centripetal acceleration. We first need to find the velocity v of the ball using the circumference of the circle (C = 2πr) and the period (T=10s). The velocity v = C/T, then we can calculate ac = v2/r, and lastly Fc = m * ac. Plugging in the values: v = 2π(0.05 m) / 10 s = 0.0314 m/s, ac = (0.0314 m/s)2 / 0.05 m = 0.01976 m/s2 and Fc = 0.4 kg * 0.01976 m/s2 = 0.0079 N. However, the correct answer is not listed among the options provided, as the correct magnitude of the centripetal force is not 0.084 N or 0.84 N. Additionally, the direction of the centripetal force is always towards the center of the circle.