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A straight metal rod of length 3 l is be...

A straight metal rod of length `3 l` is bend through the righ angle as shown. The bend rod is then placed on a rough horizontal table. A ligh string is attached to the vertex of the right angle. The string is then pulled horizontally so that the rod slides at a constant velocity. Find the angle `alpha` that side `2l` would make with the string.
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Text Solution

Verified by Experts

The correct Answer is:
`pi = tan^(-1) ((1)/(4))`
Let man of rod is `m` and friction coefficient is `mu`.
Taking moment of force about.

`Fr_(1) sin (180-alpha) l - Fr_(2) sin (alpha -90) xx(l)/(2) = 0`
`mu ((2m)/(3)) g sin alpha xx l + mu ((m)/(3)) g cos alpha xx (l)/(2) = 0`
`sin alpha = -(1)/(4) cos alpha`
`tan alpha = -(1)/(4)`
`alpha = pi - tan^(-1) (1)/(4)`.
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