A pendulum clock Which ticks 60 times is one minute on earth is placed on the moon where the acceleration due to gravity is only one - sixth of that one the earth . How many times the clock will tick over there in one minute ?

Options

A. 12.25
B. 24.5
C. 2.24
D. 0.245

Answer

To solve the problem, we need to determine how many times a pendulum clock will tick in one minute when placed on the Moon, where the acceleration due to gravity is one-sixth that of Earth.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A pendulum clock ticks 60 times in one minute on Earth.
- We need to find out how many times it ticks on the Moon, where gravity is weaker.

2. **Calculate the Time Period on Earth**:
- The time period \( T_1 \) of the clock on Earth can be calculated as:
\[ T_1 = \frac{1 \text{ minute}}{60 \text{ ticks}} = \frac{60 \text{ seconds}}{60} = 1 \text{ second} \]

3. **Time Period of a Pendulum**:
- The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Here, \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

4. **Relationship Between Time Period and Gravity**:
- Since the length \( L \) and the constant \( 2\pi \) remain the same for both Earth and the Moon, we can say:
\[ T \propto \frac{1}{\sqrt{g}} \]
- Therefore, we can write the relationship between the time periods on Earth and the Moon as:
\[ \frac{T_1}{T_2} = \sqrt{\frac{g_2}{g_1}} \]
- Where \( g_1 \) is the acceleration due to gravity on Earth and \( g_2 = \frac{g_1}{6} \) is the acceleration due to gravity on the Moon.

5. **Substituting Values**:
- Substituting \( T_1 = 1 \text{ second} \) and \( g_2 = \frac{g_1}{6} \):
\[ \frac{1}{T_2} = \sqrt{\frac{\frac{g_1}{6}}{g_1}} = \sqrt{\frac{1}{6}} \]
- This gives us:
\[ T_2 = \sqrt{6} \text{ seconds} \]

6. **Finding the Number of Ticks on the Moon**:
- The number of ticks in one minute on the Moon can be calculated as:
\[ \text{Number of ticks} = \frac{60 \text{ seconds}}{T_2} = \frac{60}{\sqrt{6}} \approx 24.5 \]

7. **Final Answer**:
- Therefore, the clock will tick approximately 24.5 times in one minute on the Moon.

### Summary:
The pendulum clock will tick approximately **24.5 times** in one minute on the Moon.