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

Options

A. `2 m`
B. `2 sqet(2 m)`
C. `sqrt5 m`
D. `(sqrt17)/(2) m`

Answer

D

Explanation

`SigmaF_(x) = 0, SigmaF_(y) = 0 therefore muN = Mg`
`Sigma tau` about `O =0`
`therefore [N(|)/(2)sintheta] (2) = muN(|)/(2) costheta`
`therefore tan theta = mu//2`
`sec theta = (sqrtmu^(2) +4)//2`
thus `((|)/(2)//1) = sqrt(mu^(2) + 4)/(2) therefore | = sqrtmu^(2) + 4`
`| = sqrt0.25 + 4 therefore | = (sqrt17)/(2)m`