Laws Of Motion Question 331

Question: A small mass slides down a fixed inclined plane of inclination 6 with the horizontal. The coefficient of friction is $ \mu ={{\mu } _{0}}x $ Where $ x $ is the distance through which the mass slides down and $ {{\mu } _{0}} $ is a constant? Then he speed is maximum after the mass covers a distance of

Options:

A) $ \frac{\cos \theta }{{{\mu } _{0}}} $

B) $ \frac{\sin \theta }{{{\mu } _{0}}} $

C) $ \frac{tan\theta }{{{\mu } _{0}}} $

D) $ \frac{2tan\theta }{{{\mu } _{0}}} $

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Answer:

Correct Answer: C

Solution:

[c] Acceleration of mass at distance x

$ a=g(\sin \theta -{{\mu } _{0}}x\cos \theta ) $

Speed is maximum, when $ a=0 $

$ g( sin\theta -{{\mu } _{0}}xcos\theta)=0 $

$ x=\frac{\tan \theta }{{{\mu } _{0}}} $



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