Question

A beam is supported at its ends by two supports which are $12\text{m}$ apart. Since the load is concentrated at its centre, there is a deflection of $3\text{cm}$ at the centre and the deflected beam is in the shape of a parabola. Then distance from the centre where deflection is $1\text{cm},$ is

• A. $24$
• B. $\sqrt{6}$
• C. $2\sqrt{6}$
• D. $6$

Answer 1

The correct option is C $2\sqrt{6}$


Let the vertex be origin and axis is $y$-axis as shown in figure.
The equation of the parabola takes the form $x^2=4ay$
Since it passes through $(6,\frac{3}{100}),$
we have $6^2=4a\times \frac{3}{100}$
$\Rightarrow a=300\text{m}$
Let $AB$ be the deflection of the beam which is $\frac{1}{100}\text{m}$
Coordinates of $B$ are $(x,\frac{2}{100})$
therefore, $x^2=4\times 300\times \frac{2}{100}$
$\Rightarrow x^2=24$
$\Rightarrow x=\pm \sqrt{24}=\pm 2\sqrt{6}$
Then distance, $|x|=2\sqrt{6}$