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JEE Main 2014 · Friction on an Incline

Friction on an Incline question from JEE Main 2014

Q27JEE Main 2014Medium

Friction on an Incline

A block of mass mm is placed on a surface with a vertical cross section given by y=x36.y = \frac{x^3}{6}. If the coefficient of friction is 0.5,0.5, the maximum height above the ground at which the block can be placed without slipping is:

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Answer: (a)

  1. Slope tan⁡θ=dydx=x22\tan\theta = \dfrac{dy}{dx} = \dfrac{x^2}{2}.
  2. No slipping limit: x22=0.5⇒x=1 m\dfrac{x^2}{2} = 0.5 \Rightarrow x = 1\text{ m}.
  3. y=136=16 my = \dfrac{1^3}{6} = \dfrac{1}{6}\text{ m}
  4. So the answer is (a) 16\dfrac{1}{6} m.
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