Two vertical walls are separated by a distance of `2` meters, Wall 'A' is smooth while wall `B` is rough with a coefficient of friction `mu=0.5`A uniform rod is probed between them. The length of the longest rod that can be probed between the walls is equal to

Options

A. `2m`
B. `2sqrt(2)m`
C. `sqrt(2)m`
D. `(sqrt(17))/2m`

Answer

D

Explanation

`muN=mg`

& `N_(1)=N_(2)`
Take the torque about the com
`N_(1)1/2sin theta+N_(2)l/2 sin theta=muN_(2)l/2cos theta`
`N_(1)1/2 sin thetaxx2=muN_(2)xxl/2cos theta`
`tan theta=mu/2, sqrt(sec^(2)theta-1)=1/2`
`sec theta=sqrt(1+(l^(2))/4), l/2=sqrt(1+0.25/4), L=sqrt(17/2)mt`