Question

A uniform stiff rod of length 300 mm and having a weight of 300 N is pivoted at one end and connected to a spring at the other end. To keep the rod vertical in a stable position the minimum value of spring constant k needed is

• A. 300 N/m
• B. 400 N/m
• C. 500 N/m
• D. 1000 N/m

Answer 1

The correct option is C 500 N/m

Let the weight be displaced from equilibrium position, then


For small displacement
$\theta =\frac{a}{300}=\frac{b}{150}$

Tanking moment about hinged point 'O'

$k.a\left(0.3\right)=W.b$

$\Rightarrow k.(0.3{)}^2=300(0.150)$

$\therefore$ $k=\frac{300\times 0.150}{(0.30{)}^2}=500\text{N/m}$