SHM 1

Classical Mechanics Level 3

Once, on free day your scientific mind, thought to perform a experiment.

You took a hollow sperical plastic ball and tied a string to it, making it a simple pendulum.Coincidencely, you were drinking PEPSI at that time.Then, you had an idea, you made a hole on the lower side of the ball and filled PEPSI in it and then sealed the hole.Then you oscillated the pendulum and noted its time period. Then, you removed the tape and emptied half of PEPSI.Then you again sealed it and measured its time period again.

What would be the change in the time period?

Decrease Cannot be determined Increase Remain the same None of these

2 solutions

Akshat Sharda
Jan 25, 2016

As the centre of mass would be shifted downwards, $l<L$ . Therefore, Time period will increase.

Great diagram.

Jake Lai - 5 years, 4 months ago

Wow nice problem!

Anik Mandal - 5 years, 4 months ago

I thought it would decrease for the mass pulling the pendulum down decreases so it can move faster... Guess I was wrong.

Bách Hữu Trần - 1 year ago

Sakshi Rathore
Jan 25, 2016

Simple, the centre of mass will be shifted downwards.

I am not sure if I am completely correct but I think there should be no change in the time period of the oscillations because of the formula T = 2π√(l/g). This suggests that the time period is independent of the mass of the object but dependent on the length of the string. So decreasing the mass won't increase the time period. Though it can alter the velocity of the motion but ultimately the energy will be conserved.

aalekh patel - 5 years, 4 months ago

I agree. The period is completely independent of mass. The length of the string and the acceleration due to gravity is all that is needed.

Matthew Voris - 5 years, 4 months ago

We know,

$T=2\pi \sqrt{\frac{l}{g}}$

Here, $g=$ acceleration due to gravity and $l=$ length of string + distance of surface to centre of gravity (hollow ball filled with pepsi in our case).

I think that the answer is correct because when the pendulum was filled fully, the centre of mass was the centre of that hollow ball but when the hollow ball was half filled with pepsi, its centre of mass must have shifted down, so $l$ have increased and thus, time period $(T)$ must also have increased.

Akshat Sharda - 5 years, 4 months ago

I thought there would be no change because the length of the string never changes, which I what I thought controlled the time?

Katlyn Allen - 5 years, 4 months ago

For a spring, isn’t the time period independent of the initial length and amplitude? T=2πsqrt(k/m)

Rohan Joshi - 4 months, 1 week ago

SHM 1

2 solutions

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