Question

The upper half of an inclined plane of inclination `45^(@)` is perfectly smooth while the lower half is rough. A block starting from rest at the top comes back to rest at the bottom. The coefficient of friction for the lower half is
A. `(1)/(sqrt(2))`
B. `1`
C. `sqrt(2)`
D. `2`

Answer 1

Correct Answer - D
Let the length of inclined plane be `d`. Speed of the block at the bottom of the upper half
`v = sqrt( 2 g sin 45^(@) xx (d)/(2)) = sqrt( g sin 45^(@) xx d)`
For the lower half , retardation : `( g sin 45^(@) - mu g cos 45^(@))`
`0 = v^(2) + 2 (g sin 45^(@) - mu g cos 45^(@)) (d)/(2)`
`= (g sin 45^(@)) d + (g sin 45^(@) - mu g cos 45^(@))d`
`0 = 1 + (1 - mu) rArr mu = 2`