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JEE Main 201815 AprilMorning ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Morning Shift
Mode
Online
Subject
Physics
Chapter
Laws of Motion

JEE Main 2018 · 15 April · Morning Shift · Online · Physics · Laws of Motion

A given object takes n times more time to slide down a 45^ rough...

A given object takes nn times more time to slide down a 45∘45^{\circ} rough inclined plane as it takes to slide down a perfectly smooth 45∘45^{\circ} incline. The coefficient of kinetic friction between the object and the incline is :

Options

  1. A1−1n2\sqrt{1-\frac{1}{n^2}}
  2. B1−1n21-\frac{1}{n^2}
  3. C12−n2\frac{1}{2-n^2}
  4. D11−n2\sqrt{\frac{1}{1-n^2}}

Correct answer

B. 1−1n21-\frac{1}{n^2}

Step-by-step solution

The coefficients of kinetic friction between the object and the incline μ=tan⁡θ\mu=\tan \theta\left(1-\frac{1}{\mathrm{n}^2}\right)⇒μ=1−1n2(∵θ=45∘)\Rightarrow \mu=1-\frac{1}{\mathrm{n}^2} \quad\left(\because \theta=45^{\circ}\right)
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