Question

A simple pendulum has a bob which is a hollow sphere full of sand and oscillated with certain period. If all that sand is drained out through a hole at its bottom, then its period (a) increases (b) decreases ( c) remains same (d) is zero.

Answer 1

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Time of the pendulum first increases and then decreases to least when the sand is completely drained from the hollow sphere (Bob).

Answer :

If we are given a simple pendulum which have a spherical Bob attached to it. If the Bob is completely filled from sand and there is a hole from which sand falls down. Now if we apply force to the pendulum first the pendulum will take more time as it is completely filled with the sand.

Whereas when the sand is running out of the hole the time interval of Bob keeps on decreasing and it will minimum when the sand is completely drained from the hollow sphere.

So, In the bottom, it's time period Decreases.

Option (b) is correct

Answer 2

The answer is Remains constant.

The time period of a simple pendulum is given by,

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

Here, l is the length of pendulum which means the distance from center of mass of pendulum bob to the other end of the pendulum.

A simple pendulum has a bob which is a hollow sphere full of sand and oscillated with certain period. Since, It is filled with sand, It is a solid sphere.

If all the sand is drained out, We have a hollow sphere.

Since Centre of mass of hollow sphere and Solid sphere of same dimensions is the same. The effective length of the simple pendulum doesn't change.

Hence, The Time period remains the same.

To note : Since the question asks for the time period after the sand is drained out, It essentially means The system is not to be observed during the draining of sand.