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 of that on Earth.

### Step-by-Step Solution:

1. **Understand the Time Period of the Pendulum Clock on Earth:**
The clock ticks 60 times in one minute, which means it completes 60 oscillations in 60 seconds. Therefore, the time period \( T \) of the pendulum on Earth is:
\[ T = \frac{60 \text{ seconds}}{60 \text{ ticks}} = 1 \text{ second} \]

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

3. **Determine the Time Period on the Moon:**
On the moon, the acceleration due to gravity \( g' \) is:
\[ g' = \frac{g}{6} \]
Substituting this into the time period formula, we get:
\[ T' = 2\pi \sqrt{\frac{L}{g'}} = 2\pi \sqrt{\frac{L}{\frac{g}{6}}} = 2\pi \sqrt{\frac{6L}{g}} = \sqrt{6} \cdot 2\pi \sqrt{\frac{L}{g}} = \sqrt{6} \cdot T \]
Since \( T = 1 \text{ second} \), we have:
\[ T' = \sqrt{6} \cdot 1 \text{ second} = \sqrt{6} \text{ seconds} \]

4. **Calculate the Number of Ticks in One Minute on the Moon:**
Now we need to find out how many ticks (oscillations) the clock will complete in 60 seconds on the moon. The number of oscillations \( N \) can be calculated using the formula:
\[ N = \frac{\text{Total Time}}{\text{Time Period}} = \frac{60 \text{ seconds}}{T'} \]
Substituting \( T' \):
\[ N = \frac{60 \text{ seconds}}{\sqrt{6} \text{ seconds}} = \frac{60}{\sqrt{6}} = 10\sqrt{6} \]

5. **Approximate the Result:**
To find the numerical value of \( 10\sqrt{6} \):
\[ \sqrt{6} \approx 2.45 \implies N \approx 10 \times 2.45 = 24.5 \]

Thus, the pendulum clock will tick approximately **24.5 times** in one minute on the moon.

### Final Answer:
The clock will tick **24.5 times** on the moon in one minute.