Question

A rod of mass m and 2l is kept vertical with one end resting on a perfectly smooth surface. when slightly disturbed from the vertical axis the rod falls as the contact point slides on the surface. based on e-l equations show that the center of mass of the rod follows a vertical trajectory

Answer 1

This is actually a tricky one since many people will end up getting

minimum force as f=μ.mgf=μ.mg

However Just read the question again , it says minimum force (There is no mention of minimum horizontal force)

Now as we know Friction force∼Normalforce∼Normal

i.e. : if we minimize the normal reaction we can minimize the friction at the same time we also need to provide enough Horizontal force to ensure block gets a horizontal velocity



Something like shown in figure !

Now the task is to find optimal angle “x” and Magnitude F

Applying simple physics : (Assuming Normal reaction from surface is N)