The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of…

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would:
  1. remain unchanged
  2. increase towards a saturation value
  3. first increase and then decrease to the original value.
  4. first decrease and then increase to the original value.

Solution

The time period of the simple pendulum is, T=2πlg Here, l is the effective length of the pendulum up to centre of mass.

When the hole at bottom of the hollow sphere (bob) filled with water is unplugged, the water will drain from the bob due to which the centre of mass will shift downward, therefore, the length of the pendulum will slightly increase, which will lead to increase in time period.

After the water completely drained out the centre of mass again shift to its original position that is up to the centre of the hollow sphere (bob) due to which the length of the pendulum will decrease and will reach to its initial state which causes the time period to reach its original value.

Asked in: AP EAMCET 2021 (20 Aug Shift 1)

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