An object takes n times as much time as to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

Question

An object takes n times as much time as to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by (A) (1-(1/n2)) (B) ((1/1-n2)) (C) √1-(1/n2) (D) √1+(1/n2)

Tardigrade Admin · Accepted Answer

The coefficient of kinetic friction between the object and the rough incline μ = tan θ(1-(1/n2)) μ = tan 45°(1-(1/n2)) =1-(1/n2)

Q. An object takes $n$ times as much time as to slide down a $4 5^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

$(1 - \frac{1}{n ^{2}})$

$(\frac{1}{1 - n ^{2}})$

$1 - \frac{1}{n ^{2}}$

$1 + \frac{1}{n ^{2}}$

The coefficient of kinetic friction between the object and the rough incline
$μ = tan θ (1 - \frac{1}{n ^{2}})$
$μ = tan 4 5^{\circ} (1 - \frac{1}{n ^{2}})$
$= 1 - \frac{1}{n ^{2}}$

Q. An object takes n times as much time as to slide down a 45∘ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

(1−n21​)