Q. There are two inclined surfaces 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 ($\mu_k$) between the object and the rough surface is close to
A) 0.25
B) 0.40
C) 0.5
D) 0.75
Explanation
[Solution by Claude - not from source] $L=\frac12at^2$, so $t_r=2t_s \Rightarrow a_r=a_s/4$. $g\sin45^\circ(1-\mu)=\frac14 g\sin45^\circ$ (since $\mu\cos45=\mu\sin45$) gives $1-\mu=\frac14$, $\mu=0.75$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.