The same mass, with a new string, is whirled in a vertical circle of the same radius about a fixed point. Find the magnitude of the tension when the mass is at the top if its speed at the top is 7.77 m/s.

256.3 N

Explanation:

Throughout the motion of the mass in the circular motion, the resultant of the Tension in the string and the weight of the body gives the net force (centripetal force) that is responsible for the acceleration of the mass in a circular motion.

At the top of the vertical circle of the motion of the mass, the tension is directed downwards towards the centre of the circle and the weight also is directed downwards towards the earth.

Net force = ma = T + W

ma = T + mg

But a = (v²/r) for circular motion,

(mv²)/r = T + mg

m = 2.31 kg

v = 7.77 m/s

r = 0.500 m

g = acceleration due to gravity = 9.8 m/s²

(2.31×7.77²)/0.5 = T + (2.31×9.8)

278.923 = T + 22.638

T = 278.923 - 22.638

T = 256.285 N = 256.3 N

Hope this Helps!!!