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.

Explanation

To solve the question regarding the effect of draining sand from a hollow sphere bob of a simple pendulum on its period, we can follow these steps:

### Step 1: Understand the Formula for the Period of a Simple Pendulum
The period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

### Step 2: Analyze the Initial Condition
Initially, the pendulum bob is a hollow sphere filled with sand. The effective mass of the bob is greater due to the sand, but the length \( L \) remains constant.

### Step 3: Consider the Effect of Draining the Sand
When the sand is drained out:
- The mass of the bob decreases, but the length \( L \) of the pendulum does not change immediately.
- As the sand drains, the distribution of mass changes, which can affect the moment of inertia and the effective length of the pendulum.

### Step 4: Determine the Immediate Effect on the Period
Initially, as the sand drains, the period of the pendulum may increase due to the change in effective length and mass distribution. However, the length \( L \) remains constant, and thus the immediate effect is that the period may increase.

### Step 5: Final Condition After All Sand is Drained
Once all the sand is drained out, the bob is now a hollow sphere with no sand inside. The effective mass distribution stabilizes, and the period of the pendulum returns to its original value, which was determined by the length \( L \).

### Conclusion
Thus, after all the sand is drained, the period of the pendulum remains the same as it was initially. Therefore, the correct answer is:
**(c) remains same.**

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