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The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
  • a)
    2 cos φ
  • b)
    2 sin φ
  • c)
    tan φ
  • d)
    2 tan φ
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The upper half of an inclined plane with inclination φ is perfectly s...
For first half
acceleration = g sin φ;
For second half
acceleration = – ( g sin φ - μg cosφ)
For the block to come to rest at the bottom, acceleration in I half = retardation in II half.
g sin φ = -(g sin φ - μg cos φ)
⇒ μ = 2 tan φ
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The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given bya)2 cos φb)2 sin φc)tan φd)2 tan φCorrect answer is option 'D'. Can you explain this answer?
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