I was given this question:
A conical pendulum is made by fixing one end of a light inextensible string to a small bob B and the other to a fixed point P. The bob is rotating in a horizontal circle with angular velocity 2 rad·s-1.
I do not know the length of the string, the mass of the bob, the
angle the string makes with the vertical, or anything!
Surprisingly, it is possible to solve this problem!
Let's start by sketching a vertical section of the pendulum.
Notice that we have given symbols to all the unknown features of the problem, each of which (except h of course!) we will try to eliminate.
Resolving vertically and horizontally:
Let us first eliminate the unknown angle from the above...
... leaving us with:
Solving (2) for T gives
And substituting into (1):
So, in this case, the correct distance is g/4