Question

A rigid bod y 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

The correct option is A

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

$m_1{r}_1+m_2{r}_2=0$
$m{r}_1=m{r}_2$
$r_1=r_2$
$\frac{\ell }{2}\cos \theta =\frac{\ell }{2}-\ell \cos \theta$
$\frac{3\ell }{2}\cos \theta =\frac{3\ell }{2}$
$\cos \theta =\frac{1}{3}$