Here's a question from ~ [ AIEEE 2002 ]

The minimum velocity ( in m/s ) with which a car driver must traverse a flat curve of radius 150 m and Coefficient of friction 0.6 to avoid skidding is ~

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As car is avoid skidding

[tex]\\ \sf\hookrightarrow \dfrac{mv^2}{r}=\mu mg[/tex]

[tex]\\ \sf\hookrightarrow \dfrac{v^2}{r}=\mu g[/tex]

[tex]\\ \sf\hookrightarrow v^2=\mu rg[/tex]

[tex]\\ \sf\hookrightarrow v^2=0.6(10)(150)[/tex]

[tex]\\ \sf\hookrightarrow v^2=60(150)[/tex]

[tex]\\ \sf\hookrightarrow v^2=900[/tex]

[tex]\\ \sf\hookrightarrow v=30ms^{-1}[/tex]

Done

The minimum velocity of the with which the car driver must traverse the flat curve to avoid skidding is 29.7 m/s.

The given parameters:

The minimum velocity of the with which the car driver must traverse the flat curve to avoid skidding is calculated as follows;

[tex]\frac{mv^2}{r} = \mu mg\\\\v^2 = \frac{\mu mgr}{m} \\\\v^2 = \mu gr\\\\v = \sqrt{\mu gr} \\\\v = \sqrt{0.6 \times 9.8 \times 150} \\\\v = 29.7 \ m/s[/tex]

Thus, the minimum velocity of the with which the car driver must traverse the flat curve to avoid skidding is 29.7 m/s.

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