Q125 / 180 · KCET 2014 · Physics
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.
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.
- AA person will slip if \( v^{2}=5 \mathrm{~ms}^{-1} \)
- Correct answerBA person will slip if \( v^{2}>5 m s^{-1} \)
- CA person will slip if \( v^{2} < 5 m s^{-1} \)
- DA person will slip if \( v^{2}>10 \mathrm{~ms}^{-1} \)
Solution
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 $5 \mathrm{~ms}^{-1}$
Hence, the correct answer is option: 'B'.