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A person is driving a vehicle at uniform speed of \( 5 \mathrm{~ms}^{-1} \) on a level curved track of radius \( 5 \mathrm{~m} \).
The coefficient of static friction between tyres and road is \( 0.1 \). Will the person slip while taking
the turn with the same speed? Take \( g=10 \mathrm{~ms}^{-2} \).
Choose the correct statement.
Options:
The coefficient of static friction between tyres and road is \( 0.1 \). Will the person slip while taking
the turn with the same speed? Take \( g=10 \mathrm{~ms}^{-2} \).
Choose the correct statement.
Solution:
2012 Upvotes
Verified Answer
The correct answer is:
A person will slip if \( v^{2}>5 m s^{-1} \)
Given, Speed of vehicle $=5 \mathrm{~ms}^{-1}$, radius of track $=5 \mathrm{~m}$, coefficient of static friction $=0.1, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}-1$ maximum
speed without slipping in given as
$\mathrm{v}_{\max }=\sqrt{\mu_{s} \times r \times g}$
Substituting the values, we get
$v_{\max }=\sqrt{0.1 \times 5 \times 10}=\sqrt{5} \Rightarrow v_{\max }^{2}=5$
Thus, the person will slip while taking the turn with the speed greater than $5 \mathrm{~ms}^{-1}$
speed without slipping in given as
$\mathrm{v}_{\max }=\sqrt{\mu_{s} \times r \times g}$
Substituting the values, we get
$v_{\max }=\sqrt{0.1 \times 5 \times 10}=\sqrt{5} \Rightarrow v_{\max }^{2}=5$
Thus, the person will slip while taking the turn with the speed greater than $5 \mathrm{~ms}^{-1}$
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