Rotational Mechanics | Advanced Problem | Sliding of a Rod in contact with Smooth Floor and Wall

A rod of length 2L leans against a wall. It starts to slip downwards without friction. Find
a) The height of the topmost point of rod when the rod loses contact with the wall.
b) Trajectory followed by centre of mass of the rod till it loses contact with the wall. Advanced problems Playlist

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[anonymouscausethatshowirol]

I felt kinda bad for not getting this problem when I first encountered it, but honestly, looking at the complexity of the derivation, I don't blame myself.

[Truthloverever]

Oh my Never imagined such a smart and tricky work😊

[NAYAN-te]

This problem was mentally beyond my comfort zone though I know every theory used in this problem solution.

[xiaohanjiang]

Thank you so much ! I am a teacher preparing students for Oxford and Cambridge interviews. This was one of the questions asked in the past!

[hrithikjyani]

good problem and a very good explanation.

[rishikeshs]

Hi Sir
Initially problem states that rod was leaning against wall.But if friction is not there how is it possible? Won't the rod fall down due to normal reaction from wall while leaning?
Plz reply Sir

[drppandey]

The component of velocity in x direction and angle found for Vx max is wrong. The V will be multiplied by Sin (phi). Check it.

[ponnapu]

sir can we coclude centre of mass is in circular motion about the corner and hence can we say it has normal acceleration towads corner and tangential acceleration perpendicular to line joinig corner and centre and hence at the time of losing contact with the wall net horizontal acceleratioon of centre of mass=0

[rmishra]

sir i was trying to find angle theta when rod looses contact with vertical wall by writing F=ma along x axis but despite considering all accelerations along x direction and making N=0 the angle coming out is absurd Sin theta = 2, i am stuck, please guide

[Prashant-fhpx]

I solved 1st part
Wrt lower end of rod by writing equation of circular motion

BTW loved your solution by using IAOR

[yanag]

how come the height of the center mass is L? If we know that the rod length is 2L but since it stands diagonally...the height of the center mass has to be Lsin(theta), no?

[blazemega]

sir energy conservation mein L ki jageh 2L ayega