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  4. A racing car of mass 1000 kg moves round a banked track at a constant speed of 108 kmh -1. Assuming the total reaction at the wheels is normal to the track and the horizontal radius of the track is 100 m , the angle of inclination of the track to the horizontal is (g=10 ms -2)

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Q. A racing car of mass 1000 kg moves round a banked track at a constant speed of $108\, kmh ^{-1}$. Assuming the total reaction at the wheels is normal to the track and the horizontal radius of the track is $100\, m$ , the angle of inclination of the track to the horizontal is $\left(g=10 \,ms ^{-2}\right)$

System of Particles and Rotational Motion

Solution:

$ \tan\, \theta=\frac{v^{2}}{Rg}$
$v=108 \,kmhr ^{-1}=108 \times \frac{5}{18} ms ^{-1}=30 \,ms ^{-1}$
$R=100 \,m$
$ \Rightarrow \tan\, \theta=\frac{30^{2}}{100 \times 10}=\frac{9}{10}$
$\theta=\tan ^{-1}\left(\frac{9}{10}\right)=42^{\circ}$