Does the value of $g$ change inside a dense fluid? How would the time period of simple pendulum change when immersed in water?

  • $\begingroup$ Neglecting viscous drag on the pendulum? $\endgroup$ – Chet Miller Mar 23 '17 at 15:46
  • $\begingroup$ Ignoring any viscous drag the upthrust will result in the effective value of $g$ being lower. $\endgroup$ – Farcher Mar 23 '17 at 16:45

The value of $g$ wouldn't change (assuming you are doing this experiment at approximately the same height above sea level as you would test an unsubmerged pendulum).

That said, the results of the experiment, and the period absolutely would change. The pendulum would have a buoyant force acting on it to slow down the movement. The density would also increase the effects of drag, so you would slow down quite a bit due to that as well.

  • $\begingroup$ Can I find out the reduced period using Newton's law? $\endgroup$ – Rajeev Modak Mar 24 '17 at 13:21
  • $\begingroup$ @RajeevModak You can use Newton's laws to determine the period. It will involve multiple extra forces acting on the pendulum besides just gravity and tension, and these forces may depend on things such a fluid dynamics. It is far more involved than the regular pendulum equation where the fluid effects can be reasonably ignored. $\endgroup$ – JMac Mar 24 '17 at 13:24

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