Answer:
The string must support the tension of 392 N.
Explanation:
The tension that the string must support should equal the centripetal force exerted on the on the stone as it goes in a circular path (because if the string supported less tension, it would break).
The centripetal force
exerted on the stone is
![F=\frac{mv^2}{R}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bmv%5E2%7D%7BR%7D)
where
<em>v</em> = velocity of the stone in m/s
<em>m</em> = mass of the stone in kg
<em>R</em> = radius of the circular path.
Now the velocity of the stone is 7.00 m/s, the mass of the stone is 4000g or 4 kg (1000 g = 1kg), and the radius of the circular path is just the length of the string, and it is 50 cm or 0.5 m (100cm =1m); therefore, we get
m = 4kg
v =7m/s
R = 0.5m.
We put these values into the equation for the centripetal force and get:
![F=\frac{(4kg)(7.00m/s)^2}{0.5}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B%284kg%29%287.00m%2Fs%29%5E2%7D%7B0.5%7D)
![\boxed{F=392N }](https://tex.z-dn.net/?f=%5Cboxed%7BF%3D392N%20%7D)
The centripetal force is 392 Newtons, and therefore, the tension that the string must support mus be 392 N.