Question

A beam is supported at its ends by supports which are $12m$ apart. Since, the load is concentrated at its centre, there is deflection of $3cm$ at the centre and the deflected beam is in the shape of a parabola. The distance between deflection of $1cm$ and the centre is

• A. $2\sqrt{6}m$
• B. $3\sqrt{6}m$
• C. $4\sqrt{6}m$
• D. $5\sqrt{6}m$

Answer 1

Answer: (A)

Let the vertex be at the lowest point and the axis vertical.

The equation of the parabola takes then form $x^2=4ay$.
Since, it passes through $\left(6,\frac{3}{100}\right)$, we have $(6{)}^2=4a\left(\frac{3}{100}\right)$ i.e., $a=36\times \frac{100}{12}=300m$.
Let $AB$ be the deflection of the beam which is $\frac{1}{100}m$.
Coordinates of $B$ are $\left(x,\frac{2}{100}\right)$.
Therefore, $x^2=4\times 300\times \frac{2}{100}=24$
i.e., $x=\sqrt{24}=2\sqrt{6}m$