Question

what happens to the time period when the bob is fiiled with mercury

Answer 1

Hi there


The period of a pendulum depends only on it’s length and the force of gravity.

The mass has nothing to do with it.

…well…unless there is air resistance (which there is). In that case, the mass of the bob does actually matter.

The real problem here is that what you say isn’t true.

The “length” of the pendulum is measured to the center of mass of the bob. If we’re talking about a simple spherical bob with a small hole in the bottom - then as the mercury drains out - the center of gravity of the bob would shift in some complicated way.

When the bob is completely full - the center of gravity would be in the center of the bob. When it’s completely empty - it’ll also be at the center. But when it’s half-full of mercury - then the center of gravity will be below the center of the spherical bob.

That would effectively lengthen the pendulum as the mercury starts to drain, then gradually shorten it again as the last of it goes away. So the period of the pendulum would actually slowly increase, then decrease again.

But as a “thought experiment” where a pendulum swinging in a vacuum has a zero-sized bob that changes slowly in mass - then indeed the period of the pendulum doesn’t change.



Thank you

Answer 2

Answer: increase

Explanation:

If water begins to drain out of the hollow sphere, its centre of mass begins to shift below thecentre of the sphere. Hence the length of the pendulum increases and time period alsoincreases. When the entire water is drained out of the sphere, the centre of mass shifts to centre.

please approve it.