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
