A uniform thin rod of mass m and length L is standing vertically along the y-axis on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbane at t = 0 causes the lower end t slip on the smooth surface along the positive x-axis, and the rod starts falling.
(i) What is the path followed by the centr of mass of the rod during its fall?
(ii) Find the equaiton to the trajectory of a point on the rod shape of the path of this point?

Answer

(i) straight line (ii) `(x^(2))/(((L)/(2) - r)^(2) ) + (y^(2))/(r^(2)) = 1`

Explanation

In the presence of gravity, the CM shifts along vertically downward direction.
For point `P : y = r sin theta`
`x = (l//2 - r) cos theta`
`1 = ((x)/((l)/(2) - r))^(2) + ((y)/(r))^(2)`