The potential energy due to the strong interaction, between two quarks or a quarkantiquark pair, goes something like v (r) = −α/r + βr, where α and β are positive constants. is there any point rv where the potential energy goes to zero? is there any point

Given that 
V= x/r + Br.
If V=0 Then -x/r + Br = 0
→ -x + br²/r = 0
→Br² - x = 0
r² = x/B
r² = +₋ √x/B
Force = dv/dr = d/dr [ -x/r +Br]
F = -[ -x/-r² + B]
= [B +x/r²]
a,B are positive.
r² is constant and it can never be negative.
∴ [ B + x/r²] is a positive value.
V = 0 at r = ⁺₋√x/B for the value of r.

Ifound this answer online hope it

The figure is missing but we can answer anyway.the correct answer is "releasing the string". in fact, when the person is holding the bow and the arrow, the kinetic energy of the arrow is still zero (because the arrow is not moving). the moment the arrow is released, it acquires a velocity v, so its kinetic energy will become different from zero: where m is the mass of the arrow and v its velocity.  all the other options, instead, do not increase the kinetic energy of the system: -  pulling farther back on the string : this will just increase the elastic potential energy of the system-  holding the arrow higher: this will increase the gravitational potential energy of the system (which is given by u=mgh, where h is the height above the ground)-  decreasing the mass of the arrow: this will decrease the gravitational potential energy of the system (which is given by u=mgh, where m is the mass)