In order to determine the tension of the rope, consider that the tension is equal to the centripetal
T = Fc - mg
Take into account that the centripetal force is given by the following formula:
Fc = 1/2·mv²/r
where
m: mass = 4.0 kg
v: speed of the mass = 5 m/s
r: radius of the circular trayectory decribes by the mass = 2 m
Look that the radius of the trayectory is equal to the length of the rope.
Replace the values of the parameters into the formula for Fc:
Fc = 1/2·(4.0 kg)(5 m/s)²/(2 m)
Fc = 25 N
The weight of the mass is:
mg = (4.0 kg)(9.8 m/s²) = 39.2 N
Hence, the tension is
T = -14.2N
