NEET · Physics · STD 11 - 4.2 friction
There are two inclined surface of equal length \((L)\) and same angle of inclination \(45^{\circ}\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction \(\left(\mu_k\right)\) between the object and the rough surface is close to:
- A 0.25
- B 0.4
- C 0.5
- D 0.75
Answer & Solution
Correct Answer
(D) 0.75
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & L=\frac{1}{2} a_S t_S^2=\frac{1}{2} a_R t_R^2 \\ \Rightarrow & \left(\frac{t_{ s }}{t_R}\right)^2=\frac{a_R}{a_{ S }} \\ \Rightarrow & \left(\frac{1}{2}\right)^2=\frac{g \sin \theta-\mu_k g \cos \theta}{g \sin \theta} \\ \Rightarrow & \frac{1}{4}=\frac{\sin 45^{\circ}-\mu_k \cos 45^{\circ}}{\sin 45^{\circ}} \\ \Rightarrow & \frac{1}{4}=\frac{\left(\frac{1}{\sqrt{2}}\right)}{\left(\frac{1}{\sqrt{2}}\right)}\left(\frac{1-\mu_k}{1}\right) \\ \Rightarrow & \frac{1}{4}=1-\mu_k \Rightarrow \mu_k=1-\frac{1}{4}=\frac{3}{4}=0.75\end{aligned}\)
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