Question

Two persons of equal height are carrying a long uniform wooden beam of length l. They are at distance $\frac{l}{5}$ and $\frac{l}{3}$. From nearest end of the rod. The ratio of normal reaction at their heads is?

• A. $4:3$
• B. $4:9$
• C. $5:9$
• D. $6:5$

Answer 1

The correct option is A $4:3$

Taking moment at point x,

$w\ast (\frac{l}{2}-\frac{l}{4})=N_2\ast (l-\frac{l}{4}-\frac{l}{6})$

$\therefore N_2=\frac{w\left(\frac{l}{4}\right)}{\left(\frac{7l}{12}\right)}$

$\therefore N_2=\frac{3w}{7}$

Now,Taking moment at point y,

$w\ast (\frac{l}{2}-\frac{l}{6})=N_1\times (l-\frac{l}{4}-\frac{l}{6})$

$\therefore N_1=\frac{w\left(\frac{l}{3}\right)}{\left(\frac{7l}{12}\right)}$

$\therefore N_1=\frac{4w}{7}$

Ratio of reaction force,

$N_1{N}_2=\frac{\frac{4w}{7}}{\frac{3w}{7}}$

$=\frac{4}{3}$