Question

In the figure shown a uniform rod of mass $m$ and length $l$ is hinged at one end & other end is connected to a light vertical spring of spring constant $k$ as shown in figure. The spring has extension such that rod is in equilibrium when it is horizontal. The rod can rotate about horizontal axis passing through end $B$. Neglecting friction at the hinge find force on the rod due to hinge.

• A. $mg$
• B. $\frac{mg}{4}$
• C. $\frac{mg}{2}$
• D. $\frac{mg}{3}$

Answer 1

The correct option is C $\frac{mg}{2}$

Given,

Rod of length, $l$ and Mass, $m$

Equilibrium in horizontal condition

Momentum at point A, $mg\frac{l}{2}-F_{c}l=0$

$F_c=\frac{mg}{2}$

Hence, vertical force on hinge is $\frac{mg}{2}$