Question

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

• A. 2 m/s
• B. 4 m/s
• C. 8 m/s
• D. 10 m/s

Answer 1

The correct option is B

4 m/s

From for diagram shown in figure,

$T_{1}cos{30}^{\circ }+T_{2}cos{45}^{\circ }=mg$ ........(i)

$T_{1}sin{30}^{\circ }+T_{2}sin{45}^{\circ }=\frac{m{v}^2}{r}$ ........(ii)

After solving equation (i) and (ii), $T_1=\frac{mg-\frac{m{v}^2}{r}}{\frac{(\sqrt{3}-1)}{2}}$

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

$v_{max}=\sqrt{1.6\times 10}$ = 4 m/s