Question

Two wires AC and BC are tied at C of small sphere of mass 5kg. which revolves at a constant speed v in the horizontal circle of radius 1.6 m. Find the maximum value of v.

Answer 1

From force diagram shown in Fig.
$T_{1}cos{30}^0+T_{2}cos{45}^0=mg$ (i)
$T_{1}sin{30}^0+T_{2}sin{45}^0=\frac{m{v}^2}{r}$ (ii)
After solving Equ. (i) and (ii),
$T_1=\frac{mg-\frac{m{v}^2}{r}}{\frac{(\sqrt{3}-1)}{2}}$

But $T_1>0,\frac{mg-\frac{m{v}^2}{r}}{\frac{\sqrt{3}-1}{2}}>0\Rightarrow mg>\frac{m{v}^2}{r}$

$\Rightarrow v<\sqrt{rg}$
$v_{max}=\sqrt{rg}=\sqrt{1.6\times 9.8}=3.96m{s}^{-1}$