# Simple pendulum with varying mass [closed]

If i make a simple pendulum using a ball filled with water and then puncture the ball with needle making a small hole. The pendulum is then made to oscillate . The water will flow through the hole . My question is that what will be the effect on time period of the pendulum? What if i replace the water with some other liquid such as glycerine or oil.

• have you tried working out the equaitons? – Jyotishraj Thoudam Feb 20 '17 at 6:19
• Think about what happens to the centre of mass of the ball and water as the water drains from the ball. – Farcher Feb 20 '17 at 7:18
• This is actually a duplicate of physics.stackexchange.com/q/80287/25301 – Kyle Kanos Jan 25 '19 at 19:50

The time period of a simple pendulum does not depend upon the mass of the bob, so it doesn't matter whether the material is solid, or a shell filled with a liquid. The time period for small oscillations is given by $T=2\pi(\sqrt{\frac{L}{g}})$ which is independent of the mass.

However, when we start draining the liquid from the bob, the center of mass of the pendulum system shifts. As the water level decreases, the center of mass will shift downward, therefore the effective length of the pendulum, which is the distance from the point of suspension to the center of mass, increases. Thus the time period will increase.

This will continue till all of the liquid has drained out of the bob. When all of the liquid drains out, the center of mass of the bob returns back to its geometrical center (assuming it to be a perfect sphere), thus the time period will decrease back to its original value, after the process is carried out.

The time period of the oscillation does not depend on the mass of the blob,

As,

$T\approx{\frac{1}{2\pi}}\sqrt{\frac{L}{g}}$

• For small oscillations – Shashaank Feb 20 '17 at 6:56
• The effective length of the pendulum changes because the centre of mass moves. – Farcher Feb 20 '17 at 8:55