JEE Mains · Physics · STD 11 - Friction
- JEE Mains 2024
- Hard
- MCQ
A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is \(0.2\) then the maximum speed with which car can negotiate the turn safely which? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(51.4 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{m}=800 \mathrm{~kg}\)
\(\mathrm{r}=300 \mathrm{~m}\)
\(\theta=30^{\circ}\)
\(\mu_2=0.2\)
\(\mathrm{~V}_{\max }=\sqrt{\operatorname{Rg}\left[\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right]}\)
\(=\sqrt{300 \times \mathrm{g} \times\left[\frac{\tan 30^{\circ}+0.2}{1-0.2 \times \tan 30^{\circ}}\right]}\)
\(=\sqrt{300 \times 10 \times\left[\frac{0.57+0.2}{1-0.2 \times 0.57}\right]}\)
\(\mathrm{V}_{\max }=51.4 \mathrm{~m} / \mathrm{s}\)
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