A beam is supported at its ends by supports which are 12 metres apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the

Explanation

Let equation of parabola is `x^(2)=ay`
It passes through the point A (600,3)
`:." "(600)^(2)=4a(3)`
`rArr" "4a=120000`
Therefore, `x^(2)=120000y`
Let at 1 cm deflection there is a point B then BO=2cm
Let the co-ordinates of B are (h,2).

B lies on parabola (1)
`:." "h^(2)=120000xx2=240000`
`rArr" "h=200sqrt(6)cm=2sqrt(6)m`
Therefore, 1 cm deflection is at a distance of `2sqrt(6)m`
from the centre.