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. The minimum value of $v$ is [image:4_image78.emf]

Question

Dr. Abubacker · Accepted Answer

(d) From force diagram shown in figure
$T_{1}\cos{30{^\circ}} + T_{2}\cos{45{^\circ}} = mg$ …(i)
$T_{1}\sin{30{^\circ}} + T_{2}\sin{45{^\circ}} = \frac{mv^{2}}{r}$ …(ii)
After solving Eq. (i) and eq. (ii), we get
$T_{1} = \frac{mg - \frac{mv^{2}}{r}}{\left( \frac{\sqrt{3} - 1}{2} ight)}$
But $T_{1} > 0$
$	herefore\frac{mg - \frac{mv^{2}}{r}}{\frac{\sqrt{3} - 1}{2}} > 0$
[image:4_image169.emf]
or $mg > \frac{mv^{2}}{r}$
or $v < \sqrt{rg}$
$	herefore\ v_{\max} = \sqrt{rg} = \sqrt{1.6 	imes 9.8} = 3.96\ ms^{- 1}$

Q. 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. The minimum value of $v$ is

Explanation

Reviewed by Dr. Abubacker

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