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AIIMS 2014
Exam
AIIMS
Year
2014
Subject
Physics
Chapter
Laws of Motion

AIIMS 2014 · Physics · Laws of Motion

A cyclist is moving in a circular track of radius 80 ~m with a...

A cyclist is moving in a circular track of radius 80 m80 \mathrm{~m} with a velocity of 36 km h−136 \mathrm{~km} \mathrm{~h}^{-1}. He has to lean from the vertical approximately through an angle (Take g=10 m s−2g=10 \mathrm{~m} \mathrm{~s}^{-2} )

Options

  1. Atan⁡−1(4)\tan ^{-1}(4)
  2. Btan⁡−1(1/8)\tan ^{-1}(1 / 8)
  3. Ctan⁡−1(1/4)\tan ^{-1}(1 / 4)
  4. Dtan⁡−1(2)\tan ^{-1}(2)

Correct answer

B. tan⁡−1(1/8)\tan ^{-1}(1 / 8)

Step-by-step solution

 Here, r=80 m,v=36kmh−1=36×(5/18)ms−1=10 m s−1\begin{array}{r}\text{ Here, } r=80 \mathrm{~m}, v=36 \mathrm{kmh}^{-1}=36 \times(5 / 18) \mathrm{ms}^{-1} \\ =10 \mathrm{~m}\mathrm{~s}^{-1}\end{array}∴tan⁡θ=v2rg=(10)280×10=18orθ=\therefore \quad \tan \theta =\frac{v^2}{r g}=\frac{(10)^2}{80 \times 10}=\frac{1}{8}or \theta=\tan ^{-1}\left(\frac{1}{8}$\right)
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