Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET 2025
Exam
NEET
Year
2025
Subject
Physics
Chapter
Laws of Motion

NEET 2025 · Physics · Laws of Motion

There are two inclined surface of equal length (L) and same angle...

There are two inclined surface of equal length (L) and same angle of inclination 45∘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 (μk)\left(\mu_k\right) between the object and the rough surface is close to :There are two inclined surface of equal length (L) and same angle of inclination 45^ with the horizontal. One of them

Options

  1. A0.250.25
  2. B0.400.40
  3. C0.50.5
  4. D0.750.75

Correct answer

D. 0.750.75

Step-by-step solution

There are two inclined surface of equal length (L) and same angle of inclination 45^ with the horizontal. One of them
L=12aStS2=12aRtR2⇒(tstR)2=aRaS⇒(12)2=gsin⁡θ−μkgcos⁡θgsin⁡θ⇒14=sin⁡45∘−μkcos⁡45∘sin⁡45∘⇒14=(12)(12)(1−μk1)⇒14=1−μk⇒μk=1−14=34=0.75\begin{aligned} & L=\frac{1}{2} a_S t_S^2=\frac{1}{2} a_R t_R^2 \\ \Rightarrow & \left(\frac{t_{\mathrm{s}}}{t_R}\right)^2=\frac{a_R}{a_{\mathrm{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}
Practice Laws of Motion on Quantrex Academy →

More from Laws of Motion

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two… NEET 2026A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of… NEET 2026A car travels on a circular racetrack of radius 50 m, which is banked at an angle θ . If… NEET 2026A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an… NEET 2025A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at 30^ ∘… NEET 2024A bob is whirled in a horizontal circle by means of a string at an initial speed of 10… NEET 2024A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A… NEET 2024A block of mass 2 ~kg is placed on an inclined rough surface AC (as shown in figure) of… NEET 2023 Full Laws of Motion list All NEET PYQs