A spring mass system has time period of `2` second. What should be the spring constant of spring if the mass of the block is `10 grams` ?

Explanation

To solve the problem, we need to find the spring constant \( k \) of a spring mass system given the time period \( T \) and the mass \( m \) of the block.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Time period \( T = 2 \) seconds
- Mass \( m = 10 \) grams

2. **Convert Mass to Kilograms:**
- Since the standard unit of mass in physics is kilograms, we need to convert grams to kilograms.
\[ m = 10 \text{ grams} = \frac{10}{1000} = 0.01 \text{ kg} \]

3. **Use the Formula for Time Period:**
- The formula for the time period \( T \) of a spring mass system is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- Rearranging the formula to solve for \( k \):
\[ T^2 = 4\pi^2 \frac{m}{k} \implies k = 4\pi^2 \frac{m}{T^2} \]

4. **Substitute the Known Values:**
- Now, substitute \( T = 2 \) seconds and \( m = 0.01 \) kg into the equation:
\[ k = 4\pi^2 \frac{0.01}{2^2} \]
- Simplifying further:
\[ k = 4\pi^2 \frac{0.01}{4} = \pi^2 \cdot 0.01 \]

5. **Calculate \( \pi^2 \):**
- The approximate value of \( \pi^2 \) is about \( 9.87 \).
\[ k \approx 9.87 \cdot 0.01 = 0.0987 \text{ N/m} \]

6. **Final Result:**
- Rounding to two decimal places, we find:
\[ k \approx 0.1 \text{ N/m} \]

### Conclusion:
The spring constant \( k \) of the spring is approximately \( 0.1 \) N/m.