Are the tension on the two strings that constrain a particle that is doing circular motion the same?

Question

may I know whether the tension on the two strings are the same, the picture is attached.

Thank you very much for your reply.

Answer 1

Suppose the tension in the upper string is $T_1$ and in the lower string $T_2$. Let the radius be $r$, the speed $v$ and the mass $m$.

Resolving vertically we get $T_1\cos\theta=T_2\cos\phi+mg$ (assuming there is gravity - leave out the $mg$ if not). Resolving horizontally we get $T_1\sin\theta+T_2\sin\phi=mv^2/r$.

So in general we do not expect $T_1=T_2$.