The correct answer is B) v_{2} = sqrt(1/2) * v_{1}.
The speed of the mass moving in a horizontal circle is given by:
v = sqrt(r * g)
where r is the radius of the circle and g is the acceleration due to gravity.
When the cord breaks, the mass will continue to move in a straight line tangent to the circle. The force causing this motion is the tension in the cord, which is proportional to the mass. Therefore, when the mass is doubled, the tension in the cord will also double.
The tension in the cord is given by:
T = M * v^2 / r
where T is the tension, M is the mass, v is the speed, and r is the radius of the circle.
Since the tension in the cord is doubled when the mass is doubled, we have:
2M * v_{2}^2 / r = M * v_{1}^2 / r
Simplifying and solving for v_{2}, we get:
v_{2} = sqrt(1/2) * v_{1}
Therefore, the new maximum speed at which the cord will break is equal to the square root of one-half times the original maximum speed.