Topic: Static and kinetic friction, laws of friction, rolling friction· Laws of Motion

There are two inclined surfaces of equal length (L) and same angle of inclination 45^° 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 smo…

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

1. 0.25

2. 0.40

3. 0.5

4. 0.75

Doubtly Asked 30 Oct 2026 NEET UG 2025 Practice test neet Save WhatsApp Report

1 answer

Best answer

Answer: 4. 0.75

Key idea: for a fixed length $L$ starting from rest, $L=\tfrac12 a t^2$, so $t\propto 1/\sqrt a$.

Smooth plane: $a_s=g\sin45^\circ$. Rough plane: $a_r=g(\sin45^\circ-\mu\cos45^\circ)$.

Since $t_r=2t_s$, we get $a_r=a_s/4$:

$$g\sin45^\circ(1-\mu)=\frac{g\sin45^\circ}{4}\Rightarrow 1-\mu=\frac14\Rightarrow \mu=0.75$$

(At $45^\circ$, $\sin$ and $\cos$ are equal, so they cancel.)

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

Was this answer helpful?

There are two inclined surfaces of equal length (L) and same angle of inclination 45^° 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 smo…

1 answer

Your answer