Question

A circular ring of radius 'r' meters is suspended from a point 'h' meters vertically above the center of ring by four strings of equal lengths attached at equal intervals to the circumference of the ring. If '$\theta$' be the angle between two consecutive strings, then cos $\theta$ is equal to :

• A. $\frac{h^2}{h^2+r^2}$
• B. $\frac{r^2}{h^2+r^2}$
• C. $\frac{{2h}^2}{h^2+r^2}$
• D. $\frac{{2r}^2}{h^2+r^2}$

Answer 1

Answer: (A)

$\frac{h^2}{h^2+r^2}$

$l=\sqrt{h^2+r^2}$

$x=\sqrt{r^2+r^2}=\sqrt{2r^2}$

$\Rightarrow \cos \theta =\frac{l^2+l^2-x^2}{2l^2}$

$\Rightarrow \cos \theta =\frac{l^2-r^2}{l^2}$

$\Rightarrow \cos \theta =\frac{h^2+r^2-r^2}{h^2+r^2}$

$\Rightarrow \cos \theta =\frac{h^2}{h^2+r^2}$

Hence, option $\left(A\right)$ is correct answer.