One - fourth length of a uniform rod is placed on a rough horizontal surface and it starts rotating about the edge as soon as we release it. The rod starts slipping on the edge when it has turned through an angle `theta`. If the coefficient of friction between rod and surface is `mu`, and it satisfies the relation `x tan theta=4mu`, then what is the value of x? `["Take "g=10m//s^(2)]`

Answer

13

Explanation

`(mgl)/(4) sin theta = (1)/(2) I omega ^(2)`

`mu N - mg sin theta = m omega ^(2) (1)/(4)`
`mg cos theta - N = m (1)/(4) alpha`
Solving,
`13 tan theta =4 mu `
`implies x = 13`