What is the maximum velocity that a 0.3–kilogram mass attached to a 0.75–meter string can have if the mass is whirled around in a circular horizontal path? the maximum tension that the string can withstand is 250 newtons.

Since this is a horizontal path, we can neglect the force of gravity acting on the body. So in this case we have that the force of tension is equal to the centripetal force, because we have a circular path. 

Fcp=T, where T is the force of tension and Fcp is the centripetal force. 

m*(v²/R)=250 N, where m is the mass of the body and it is m=0.3 kg, v is the max speed of the body, and that is what we are looking for and R is the max length of the string and it is R=0.75 m. 

We divide by m and multiply by R and we get:

v²=(250*R)/m, take the square root:

v=√((250*R)/m)=25 m/s

So the max speed of the body if the max tension is T= 250 N and its max length is R=0.75 m is V=25 m/s. 

What does the start look like