JEE MAIN - Physics (2005 - No. 41)
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
first decrease and then increase to the original value
first increase and then decrease to the original value
increase towards a saturation value
remain unchanged
Explanation
Center of mass of combination of liquid and hollow portion (at position $$\ell $$ ), first goes down (to $$\ell + \Delta \ell $$) and when total water is drained out, center of mass regain its original position (to $$\ell $$),
$$$T = 2\pi \sqrt {{\ell \over g}} $$$
$$\therefore$$ $$'T'$$ first increases and then decreases to original value.
$$\therefore$$ $$'T'$$ first increases and then decreases to original value.
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