# At what height will the tension of the string attached to a bob which was given an initial velocity from the bottom become zero?

Assuming a bob attached to a string is given a horizontal velocity u when it is at the bottom, what would be the height at which the tension of the bob would be zero (i.e the bob leaves the circular path). I know that the cos component of weight should be equal to the centripetal force, but I cannot formulate an equation for it. Any suggestions?

• Do you mean "string"? If "spring" it will not be a circular path. – Ben51 Jan 7 '18 at 5:15
• Yeah😅! I meant a string – Roshan Surana Jan 7 '18 at 7:10

I'm assuming that you're looking for the radius needed to achieve velocity v:

$F=ma$

$F_G + F_T = m v^2 / r$

$mg = mv^2 / r$

$g= v^2/r$

$r = v^2/g$

The radius needed is velocity (tangent to acceleration) squared divided by gravity acceleration