The pendulum of a clock is replaced by a spring mass system with the spring having spring constant `0.1Nm^-1`. What mass should be attached to the spring?

Explanation

To solve the problem of finding the mass that should be attached to the spring in order to match the time period of the pendulum clock, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Time Period of the Pendulum**:
The time period of the pendulum clock is given as \( T = 2 \) seconds.

2. **Write the Formula for the Time Period of a Spring-Mass System**:
The time period \( T' \) of a spring-mass system is given by the formula:
\[ T' = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass attached to the spring and \( k \) is the spring constant.

3. **Set the Time Periods Equal**:
Since we want the time period of the spring-mass system to be the same as that of the pendulum, we set:
\[ T' = T \]
Therefore:
\[ 2\pi \sqrt{\frac{m}{k}} = 2 \]

4. **Simplify the Equation**:
Divide both sides by \( 2 \):
\[ \pi \sqrt{\frac{m}{k}} = 1 \]
Now, divide both sides by \( \pi \):
\[ \sqrt{\frac{m}{k}} = \frac{1}{\pi} \]

5. **Square Both Sides**:
Squaring both sides gives:
\[ \frac{m}{k} = \frac{1}{\pi^2} \]

6. **Solve for Mass \( m \)**:
Rearranging the equation gives:
\[ m = \frac{k}{\pi^2} \]

7. **Substitute the Value of \( k \)**:
Given that the spring constant \( k = 0.1 \, \text{N/m} \):
\[ m = \frac{0.1}{\pi^2} \]

8. **Calculate \( \pi^2 \)**:
The approximate value of \( \pi^2 \) is about \( 10 \) (since \( \pi \approx 3.14 \)):
\[ m \approx \frac{0.1}{10} = 0.01 \, \text{kg} \]

9. **Convert to Grams**:
Since \( 1 \, \text{kg} = 1000 \, \text{g} \):
\[ m = 0.01 \, \text{kg} = 10 \, \text{g} \]

### Final Answer:
The mass that should be attached to the spring is **10 grams**.