The second's pendulum is taken from earth to moon, to keep time period constant
(a) the length of the second's pendulum should be decreased
(b) the length of the second's pendulum should be increased
( c) the amplitude should increase
(d) the amplitude should decrease.

Explanation

To solve the problem of how to keep the time period of a second's pendulum constant when moving from Earth to the Moon, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Time Period**:
The time period \( T \) of a pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Identify the Variables**:
- On Earth, let the length of the pendulum be \( L_e \) and the gravitational acceleration be \( g_e \).
- On the Moon, let the length of the pendulum be \( L_m \) and the gravitational acceleration be \( g_m \).

3. **Set Up the Equation for Constant Time Period**:
Since the time period needs to remain constant when moving from Earth to the Moon, we can set the time periods equal to each other:
\[ T_e = T_m \]
This implies:
\[ 2\pi \sqrt{\frac{L_e}{g_e}} = 2\pi \sqrt{\frac{L_m}{g_m}} \]
We can cancel \( 2\pi \) from both sides:
\[ \sqrt{\frac{L_e}{g_e}} = \sqrt{\frac{L_m}{g_m}} \]

4. **Square Both Sides**:
Squaring both sides gives:
\[ \frac{L_e}{g_e} = \frac{L_m}{g_m} \]

5. **Rearranging the Equation**:
Rearranging the equation leads to:
\[ L_e \cdot g_m = L_m \cdot g_e \]
Therefore, we can express the length on the Moon in terms of the length on Earth:
\[ L_m = \frac{L_e \cdot g_m}{g_e} \]

6. **Substituting the Values of Gravity**:
We know that the acceleration due to gravity on the Moon \( g_m \) is approximately \( \frac{1}{6} g_e \). Substituting this into the equation gives:
\[ L_m = \frac{L_e \cdot \left(\frac{1}{6} g_e\right)}{g_e} = \frac{L_e}{6} \]

7. **Conclusion**:
This means that to keep the time period constant when moving from Earth to the Moon, the length of the second's pendulum must be decreased to one-sixth of its original length on Earth. Thus, the correct answer is:
**(a) the length of the second's pendulum should be decreased.**