A piece of ics slides down a `45^(@)` incline in twice the time it takes to slide down a frictionless `45^(@)` incline . What is the coefficient of friction between the ice and the incline ? .

Answer

`mu = 0.75`

Explanation

On a rough incline
`a = " g sin" theta - mu "g cos" theta `
On a smooth incline
`a' = " g sin " theta `
Now , if L = length of incline
Then , `L = (1)/(2) a xx (2t)^(2)`
`L = (1)/(2) a't^(2)`
`therefore " " (1)/(2)a xx 4 t^(2) = (1)/(2)a't^(2)`
` 4 ( "g sin" theta - mu "g cos" theta ) = "g sin" theta`
3 sin `theta = 4 mu "cos" theta `
`mu = (3)/(4)`