pls derive the formula of radius of curvature i e R = l2/6h+h/2 - Physics - Units And Measurements

Question

pls derive the formula of radius of curvature i e R =
l2/6h+h/2

Jyoti Pant · Accepted Answer

Here AEXFY is the sphere of which the given spherical surface forms a part DE=h=height of the central screw above the plane of the outer legs

From the circle geometry, ${A D}^{2} = E D D F r^{2} = h (2 R - h) o r R = \frac{r^{2}}{2 h} + \frac{h}{2}$

$N o w i n t h e a b o v e f i g u r e, l = l e n g t h o f e a c h s i d e o f t h e e q u i l a t e r a l t r i a n g l e f o r m e d b y j o i n g t h e t i p s o f l e g s S o, \frac{l}{2} = r \cos 30^{0} = \frac{r \sqrt{3}}{2} o r r = \frac{l}{\sqrt{3}} T h e r e f o r e w e h a v e, R = \frac{l^{2}}{6 h} + \frac{h}{2}$

pls derive the formula of radius of curvature i.e. R = l2/6h+h/2