The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A body released from rest from the top comes to rest at the bottom if the coefficient of friction for the lower half is given by:-

Step-by-step solution

For upper half v 2 = v 2 + 2 a l / 2 = 2 ( g sin θ ) 1 / 2 = g l sin θ For lower half 0 = v 2 + 2 g ( sin θ - μ cos θ ) 1 2 ⇒ - g l sin θ = g l ( sin θ - μ cos θ ) ⇒ μ cos θ = 2 sin θ ⇒ μ = 2 tan θ