1.

A block takes a twice as much time to slide down a `45^(@)` rough inclined plane as it takes to slide down a similar smooth , plane . The coefficient of friction is :A. `(3)/(4)`B. `(sqrt3)/(2)`C. `(1)/(4)`D. `(1)/(3)`

Answer» Correct Answer - A
l = `(1)/(2) a_(1) t_(1)^(2) = (1)/(2) a_(2)t_(2)^(2)`
`(1)/(2) ( "g cos" theta) t^(2) = (1)/(2) g ( "sin" theta - mu "cos" theta ) 4t^(2)`
`"cos" 45^(@) = 4 ( "sin" 45^(@) - mu "cos" 45^(@))`
`(1)/(sqrt2) = 4 ((1)/(sqrt2) - (mu)/(sqrt2))`
`1 = 4 (1 - mu)`
`mu = (3)/(4)`


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