A glass plate breaks when a mass of 3 kg or more is kept on it. An iron piece is kept on that plate in a lift. If the upward acceleration of the lift is gradually increased to 245cm * s ^ - 2 the plate breaks. What is the mass of the imn piece?

Given:
- A glass plate breaks when a mass of 3 kg or more is placed on it.
- An iron piece is placed on the plate in a lift.
- The lift's upward acceleration is gradually increased to \(245 \text{ cm/s}^2\) (which is equivalent to \(2.45 \text{ m/s}^2\)).
- The plate breaks under these conditions.

We need to find the mass of the iron piece.

### Step-by-Step Solution

1. **Convert the upward acceleration to meters per second squared:**

   \[
   245 \text{ cm/s}^2 = 2.45 \text{ m/s}^2
   \]

2. **Calculate the effective acceleration:**

   When the lift is accelerating upwards, the effective acceleration (a') acting on the iron piece is the sum of the gravitational acceleration (\(g\)) and the lift's acceleration (\(a\)):

   \[
   a' = g + a
   \]

   Given:
   \[
   g = 9.8 \text{ m/s}^2
   \]
   \[
   a = 2.45 \text{ m/s}^2
   \]

   So,
   \[
   a' = 9.8 \text{ m/s}^2 + 2.45 \text{ m/s}^2 = 12.25 \text{ m/s}^2
   \]

3. **Determine the effective weight (W') of the iron piece:**

   The weight of the iron piece is the force due to gravity, which is:
   \[
   W = mg
   \]

   However, with the lift's acceleration, the effective weight becomes:
   \[
   W' = ma'
   \]

4. **Set up the condition for the plate breaking:**

   The plate breaks under an effective weight corresponding to 3 kg under normal gravity:
   \[
   3 \text{ kg} \times 9.8 \text{ m/s}^2 = 29.4 \text{ N}
   \]

   Therefore, the effective weight \(W'\) must also be 29.4 N:
   \[
   W' = m \times 12.25 \text{ m/s}^2 = 29.4 \text{ N}
   \]

5. **Solve for the mass (m) of the iron piece:**

   \[
   m \times 12.25 \text{ m/s}^2 = 29.4 \text{ N}
   \]
   \[
   m = \frac{29.4 \text{ N}}{12.25 \text{ m/s}^2}
   \]
   \[
   m \approx 2.4 \text{ kg}
   \]

### Conclusion

The mass of the iron piece is approximately \(2.4 \text{ kg}\).

Would you like more details or have any questions?

Here are 5 more questions you might consider:
1. What is the difference between weight and mass?
2. How do you calculate the net force on an object in an accelerating lift?
3. What is the significance of the gravitational constant (\(g\)) in physics problems?
4. How does acceleration affect the apparent weight of an object?
5. Can you explain how to convert units from cm/s\(^2\) to m/s\(^2\)?

**Tip:** Always ensure to convert units to a consistent system (e.g., SI units) when solving physics problems.

Learn how to calculate the mass of an iron piece placed in a lift accelerating upwards using Newton's second law and gravitational force formula. Solve this physics problem step-by-step with detailed explanations.

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