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Motion in Straight Line

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30o, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be respectively

  • 0.6 and 0.6

  • 06 and 0.5

  • 0.5 and 0.6 

  • 0.4 and 0.3


B.

06 and 0.5

Given a plank with a box on it one end is gradually raised about the end having angle of inclination is 300, the box starts to slip and slides down  4 m the plank in 4 s as shown in a figure.



The coefficient of static friction.

straight mu subscript straight s space equals space tan space 30 to the power of straight o space equals space fraction numerator 1 over denominator square root of 3 space end fraction space equals space 0.6
So, distance covered by a plank,
straight s space equals space ut space plus space 1 half at squared
Here comma space straight u space equals space 0 space and space straight a space equals space straight g space left parenthesis sinθ space minus space straight mu space cos space straight theta right parenthesis
therefore space 4 space equals space 1 half space straight g space left parenthesis sin space 30 space space minus space straight mu subscript straight k space cos space 30 right parenthesis space left parenthesis 4 right parenthesis squared

rightwards double arrow space 0.5 space straight x space 10 space straight x space 1 half straight x space minus straight mu subscript straight k space straight x space 10 space straight x fraction numerator square root of 3 over denominator 2 end fraction
rightwards double arrow space 5 square root of 3 space straight mu subscript straight k space equals space 4.5 space rightwards double arrow space straight mu subscript straight k space equals space 0.51

Thus, coefficient of kinetic friction between the box and the plank is 0.51


Given a plank with a box on it one end is gradually raised about the end having angle of inclination is 300, the box starts to slip and slides down  4 m the plank in 4 s as shown in a figure.



The coefficient of static friction.

straight mu subscript straight s space equals space tan space 30 to the power of straight o space equals space fraction numerator 1 over denominator square root of 3 space end fraction space equals space 0.6
So, distance covered by a plank,
straight s space equals space ut space plus space 1 half at squared
Here comma space straight u space equals space 0 space and space straight a space equals space straight g space left parenthesis sinθ space minus space straight mu space cos space straight theta right parenthesis
therefore space 4 space equals space 1 half space straight g space left parenthesis sin space 30 space space minus space straight mu subscript straight k space cos space 30 right parenthesis space left parenthesis 4 right parenthesis squared

rightwards double arrow space 0.5 space straight x space 10 space straight x space 1 half straight x space minus straight mu subscript straight k space straight x space 10 space straight x fraction numerator square root of 3 over denominator 2 end fraction
rightwards double arrow space 5 square root of 3 space straight mu subscript straight k space equals space 4.5 space rightwards double arrow space straight mu subscript straight k space equals space 0.51

Thus, coefficient of kinetic friction between the box and the plank is 0.51


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