Starting from rest, the time taken by a body sliding down on a rough inclined plane at 45° with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is

Question

Starting from rest, the time taken by a body sliding down on a rough inclined plane at 45° with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is (A) 0.25 (B) 0.33 (C) 0.50 (D) 0.75

Tardigrade Admin · Accepted Answer

μ= tan θ 1-(1/n2) Here, θ=45° and n=2 ∴ μ= tan 45° 1-(1/22) =1-(1/4)=(3/4)=0.75

Q. Starting from rest, the time taken by a body sliding down on a rough inclined plane at $4 5^{\circ}$ with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is

0.25

0.33

0.50

0.75

$μ = tan θ 1 - \frac{1}{n ^{2}}$
Here, $θ = 4 5^{\circ}$ and $n = 2$
$∴ μ = tan 4 5^{\circ} 1 - \frac{1}{2 ^{2}}$
$= 1 - \frac{1}{4} = \frac{3}{4} = 0.75$

Q. Starting from rest, the time taken by a body sliding down on a rough inclined plane at 45∘ with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is