Q: The upper half of an inclined plane with inclination of φ is perfectly smooth while the lower half is rough. A body at the top starts from rest will again come to rest at the bottom, the coefficient of friction for the lower half if given by
(a) 2 tanφ
(b) tanφ
(c) 2 sinφ
(d) 2 cosφ
Click to See Answer :
Ans: (a)
Sol: For upper half :
$v^2 = u^2 + 2 a s $
$v^2 = 0 + 2 (g sin\phi) (\frac{d}{2}) $ …(i)
For Lower half :
$0 = v^2 + 2(g sin\phi – \mu g cos\phi) (\frac{d}{2}) $ …(ii)
From (i) ,
$ 0 = 2 (g sin\phi) (\frac{d}{2}) + 2(g sin\phi – \mu g cos\phi) (\frac{d}{2}) $
$ 0 = 2 sin\phi – \mu cos\phi $
$\mu = 2 tan\phi $