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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2020 · 4 September · Evening Shift · Physics · Motion in One Dimension

A small ball of mass m is thrown upward with velocity u from the...

A small ball of mass mm is thrown upward with velocity uu from the ground. The ball experiences a resistive force mkv2mk{v}^{2} where vv is it speed. The maximum height attained by the ball is :

Options

  1. A12ktan⁡−1ku2g\dfrac{1}{2k}\tan^{- 1}\dfrac{k{u}^{2}}{g}
  2. B1kln⁡(1+ku22g)\dfrac{1}{k}\ln \left(1 + \dfrac{k{u}^{2}}{2g}\right)
  3. C1ktan⁡−1ku22g\dfrac{1}{k}\tan^{- 1}\dfrac{k{u}^{2}}{2g}
  4. D12kln⁡(1+ku2g)\dfrac{1}{2k}\ln \left(1 + \dfrac{k{u}^{2}}{g}\right)

Correct answer

D. 12kln⁡(1+ku2g)\dfrac{1}{2k}\ln \left(1 + \dfrac{k{u}^{2}}{g}\right)

Step-by-step solution

Fne=ma{F}_{\text{ne}} = ma

−mg−mkv2=mvdvds- mg - {mkv}^{2} = mv\dfrac{dv}{ds}

vdvds=−g−kv2v\dfrac{dv}{ds} = - g - {kv}^{2}

- {∫}_{{v}_{0}}^{0}\dfrac{vdv}{g + {kv}^{2}} = {∫}_{0}^{h}ds = {h}_\max

{h}_\max = \dfrac{1}{2K} in \left(\dfrac{g + {kv}_{0}^{2}}{g}\right)

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