# A ball is thrown upward with an initial velocity $\mathrm{V}_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m \gamma v^{2}$ (where $m$ is mass of the ball, $v$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is:

Question:

A ball is thrown upward with an initial velocity $\mathrm{V}_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m \gamma v^{2}$ (where $m$ is mass of the ball, $v$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is:

1. $\frac{1}{\sqrt{\gamma g}} \tan ^{-1}\left(\sqrt{\frac{\gamma}{g}} \mathrm{~V}_{0}\right)$

2. $\frac{1}{\sqrt{\gamma} g} \sin ^{-1}\left(\sqrt{\frac{\gamma}{g}} \mathrm{~V}_{0}\right)$

3. $\frac{1}{\sqrt{\gamma g}} \ln \left(1+\sqrt{\frac{\gamma}{g}} \mathrm{~V}_{0}\right)$

4. $\frac{1}{\sqrt{2 \gamma} g} \tan ^{-1}\left(\sqrt{\frac{2 \gamma}{g}} \mathrm{~V}_{0}\right)$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Laws of Motion chapter.

JEE Main Previous Year 10 April 2019

Correct Option: 1

Solution:

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