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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Physics
Chapter
Laws of Motion

JEE Main 2005 · Physics · Laws of Motion

A smooth block is released at rest on a 45^ incline and then slides...

A smooth block is released at rest on a 45∘45^{\circ} incline and then slides a distance d. The time taken to slide is n\mathrm{n} times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

Options

  1. Aμk=1−1n2\mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^2}
  2. Bμk=1−1n2\mu_{\mathrm{k}}=\sqrt{1-\frac{1}{\mathrm{n}^2}}
  3. Cμs=1−1n2\mu_s=1-\frac{1}{n^2}
  4. Dμs=1−1n2\mu_s=\sqrt{1-\frac{1}{n^2}}

Correct answer

A. μk=1−1n2\mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^2}

Step-by-step solution

d=12g2t12\mathrm{d}=\frac{1}{2} \frac{\mathrm{g}}{\sqrt{2}} \mathrm{t}_1^2  d=12g2(1−μk)t22\mathrm{~d}=\frac{1}{2} \frac{\mathrm{g}}{\sqrt{2}}\left(1-\mu_{\mathrm{k}}\right) \mathrm{t}_2^2 t22t12=n2=11−μk\frac{\mathrm{t}_2^2}{\mathrm{t}_1^2}=\mathrm{n}^2=\frac{1}{1-\mu_{\mathrm{k}}}
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