Question

The end 'A' of a uniform rod AB of length 'l' touches a horizontal smooth fixed surface. Initially the rod makes an angle of ${30}^o$ with the vertical. Find the magnitude of displacement of the end B just before it touches the ground after the rod is released.

Answer 1

When the rod is released, it falls due to gravity so no external force acts along horizontal direction, and so, CM will not displace along horizontal.

$\Rightarrow$ Initial horizontal list of B from $CM=\frac{l}{2}\sin 3\theta$

Final horizontal dist. of B from $CM=\frac{l}{2}$

$\therefore$ Magnitude of disp. of the end B just before it touches the ground is $:\frac{13l}{4}.$