Q125 / 160 · AP EAMCET 2023 (17 May Shift 1) · Physics

A lorry is moving on a smooth circular path of radius 50 $\mathrm{m}$ with a velocity of $20 \mathrm{~ms}^{-1}$. Then the banking angle of the road is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

  • A
    $\tan ^{-1} \frac{5}{4}$
  • Correct answer
    B
    $\tan ^{-1} \frac{4}{5}$
  • C
    $\tan ^{-1} \frac{2}{5}$
  • D
    $\tan ^{-1} \frac{5}{2}$

Solution

Radius of circular path, $R=50 \mathrm{~m}$ Velocity, $V=20 \mathrm{~m} / \mathrm{s}$ Banking angle of the road, $\tan \theta=\frac{V^2}{R g}$ $\theta=\tan ^{-1}\left(\frac{20^2}{50 \times 10}\right)=\tan ^{-1}\left(\frac{4}{5}\right)$

Hence, the correct answer is option: 'B'.

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