Question

A rigid body in the shape of a $V$ has two equal arms made of uniform rods.What must the angle between the two rods be so that when the body is suspended from one end, the other arm is horizontal?

• A. ${\cos }^{-1}\left(\frac{1}{3}\right)$
• B. ${\cos }^{-1}\left(\frac{1}{2}\right)$
• C. ${\cos }^{-1}\left(\frac{1}{4}\right)$
• D. ${\cos }^{-1}\left(\frac{1}{6}\right)$

Answer 1

Answer: (A)

${\cos }^{-1}\left(\frac{1}{3}\right)$

Center of mass must be below point P as the system is in equilibrium

Length of both rods are equal (l) and also the mass (m).

$X_{cm}=\frac{m\left(l/2\right)+m\left(l/2\right)Cos\theta }{m+m}=lCos\theta$

So, $1+lcos\theta =4lcos\theta$

$cos\theta =\frac{1}{3}$