1.

A smooth block is released at rest on a 45^(@) incline and then slides a distance 'd'. The time taken to slide is 'n' times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

Answer»

`mu_(k)=1-(1)/(n^(2))`
`mu_(k)=SQRT(1-(1)/(n^(2)))`
`mu_(s)=1-(1)/(n^(2))`
`mu_(s)=sqrt(1-(1)/(n^(2)))`

Solution :On smooth incline plane
`d=(1)/(2)g SINN THETA xxt^(2)`
On rough incline plane
`d=(1)/(2)g(sin theta-mu_(k) COS theta) (nt)^(2)...(b)`
SOLVING equations (a)and(b)
`sin theta=n^(2)(sintheta-mu_(k) cos theta)`and Putting `theta=45^(@)`
we get `mu_(k)=1-(1)/(n^(2))`


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