Question

Derive the formula mv²/r
(Class XI - Kinemetics- Circular Motion)

Answer 1

 h(2R-h) = x2 
but 2R>> h therefore 2h = x2 and so h = x2/2R (equation 1) 
now x = AK which is almost the arcAB = vt (equation 2) 
 
Combining 1 and 2, h = (vt)2/2R (equation 3) 
h is the vertical fall and so using s = 1/2 at2 = h (equation 4) 
 
Then from (3) and (4) 1/2at2 = (vt)2/2R leading to a = v2/R 
Using F = ma then F = mv2/R