Given, radius of horizontal circle,
r= Figure illustrating the particle of mass m moving in a horizontal circle, while suspended from a ceiling is shown
In equilibrium condition at point A,
Tcosθ=mg ...(i)
Tsinθ= ...(ii)
Divide Eq. (ii) by Eq. (i),
tanθ=v2∕rg ⇒v=√rgtanθ ...(iii)
Now, from figure, we can write
sinθ== ⇒ θ = 45°
Substituting the value of θ in Eq. (iii), we get
v=√rgtan45°=√rg Thus, the value of speed of particle is
v=√rg.