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

Question

The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient of kinetic friction between the object and the incline plane is (A) √(1/1- n 2) (B) √1-(1/n2) (C) 1+(1/n2) (D) 1-(1/n2)

Tardigrade Admin · Accepted Answer

a 1= g sin θ= g / √2 a 2= g sin θ- Kg cos θ=( g /√2)-( Kg /√2) t 2= nt 1 a 1 t 12= a 2 t 22 ( g /√2) t 12=(( g /√2)-( kg /√2)) n 2 t 12 K =1-(1/ n 2)

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

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

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

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

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

$a_{1} = g sin θ = g / 2$
$a_{2} = g sin θ - K g cos θ = \frac{g}{2} - \frac{K g}{2}$
$t_{2} = n t_{1} & a_{1} t_{1}^{2} = a_{2} t_{2}^{2}$
$\frac{g}{2} t_{1}^{2} = (\frac{g}{2} - \frac{k g}{2}) n^{2} t_{1}^{2}$
$K = 1 - \frac{1}{n ^{2}}$

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

1−n21​​

1−n21​​

1+n21​

1−n21​

a1​=gsinθ=g/2​ a2​=gsinθ−Kgcosθ=2​g​−2​Kg​ t2​=nt1​&a1​t12​=a2​t22​ 2​g​t12​=(2​g​−2​kg​)n2t12​ K=1−n21​

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

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

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

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

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

$a_{1} = g sin θ = g / 2$
$a_{2} = g sin θ - K g cos θ = \frac{g}{2} - \frac{K g}{2}$
$t_{2} = n t_{1} & a_{1} t_{1}^{2} = a_{2} t_{2}^{2}$
$\frac{g}{2} t_{1}^{2} = (\frac{g}{2} - \frac{k g}{2}) n^{2} t_{1}^{2}$
$K = 1 - \frac{1}{n ^{2}}$