Duration: 2:58

66 views

2

A ball is thrown upward with an initial velocity \( v_{0} \) 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
[JEE (Main) 2019]
(a) \( \frac{1}{\sqrt{\gamma g}} \tan ^{-1}\left(\sqrt{\frac{\gamma}{g}} v_{0}\right) \)
(b) \( \frac{1}{\sqrt{\gamma g}} \ln \left(1+\sqrt{\frac{\gamma}{g}} v_{0}\right) \)
(c) \( \frac{1}{\sqrt{\gamma g}} \sin ^{-1}\left(\sqrt{\frac{\gamma}{g}} v_{0}\right) \)
(d) \( \frac{1}{\sqrt{2 \gamma g}} \tan ^{-1}\left(\sqrt{\frac{2 \gamma}{g}} v_{0}\right) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live