### Laws Of Motion Question 6

#### Question 6 - 29 January - Shift 2

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

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

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

(3) $1+\frac{1}{n^{2}}$

(4) $1-\frac{1}{n^{2}}$

## Show Answer

#### Answer: (4)

#### Solution:

#### Formula: Wedge Constraint

$a_1=g \sin \theta=g / \sqrt{2}$

$a_2=g \sin \theta-Kg \cos \theta=\frac{g}{\sqrt{2}}-\frac{Kg}{\sqrt{2}}$

$t_2=nt_1 \quad and \quad a_1 t_1^{2}=a_2 t_2^{2}$

$\frac{g}{\sqrt{2}} t_1^{2}=(\frac{g}{\sqrt{2}}-\frac{kg}{\sqrt{2}}) n^{2} t_1^{2}$

$K=1-\frac{1}{n^{2}} \quad$ Ans. 4