Ten one-rupee coins are put on top of each other on a table, Each coin has a mass m. Which of the following statements in not ture?

Options

A. The force on the `7^(th)` coin due to `8^(th)` coin is 3mg (downwards)
B. The force on the `6^(th)` coin due to `7^(th)` coin is 4mg (downwards)
C. The reaction of the 6th coin on the `7^(th)` coin is 4mg (upward)
D. The total force on the `10^(th)` coin is `9mg` (downwards)

Explanation

To determine which statement is not true regarding the ten one-rupee coins stacked on top of each other, we will analyze the forces acting on each coin based on Newton's laws of motion.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have 10 coins stacked vertically, each with a mass \( m \).
- The total mass of coins above any given coin will affect the force acting on that coin.

2. **Analyzing the Forces on the 7th Coin**:
- The coins above the 7th coin are the 8th, 9th, and 10th coins.
- Each of these coins has a mass \( m \), so the total mass above the 7th coin is \( 3m \).
- The force acting on the 7th coin due to the coins above it (8th, 9th, and 10th) is given by the weight of these coins:
\[ F = 3m \cdot g = 3mg \text{ (downward)} \]
- This confirms that the statement about the force on the 7th coin is true.

3. **Analyzing the Forces on the 6th Coin**:
- The coins above the 6th coin are the 7th, 8th, 9th, and 10th coins.
- The total mass above the 6th coin is \( 4m \).
- The force acting on the 6th coin due to the coins above it is:
\[ F = 4m \cdot g = 4mg \text{ (downward)} \]
- This confirms that the statement about the force on the 6th coin is also true.

4. **Analyzing the Normal Force on the 7th Coin**:
- The normal force exerted by the 6th coin on the 7th coin is equal to the force that the 7th coin exerts on the 6th coin, which is \( 4mg \) (upward).
- According to Newton's third law, the reaction force is equal in magnitude and opposite in direction.
- Thus, the normal force on the 7th coin is \( 4mg \) (upward), confirming that this statement is true.

5. **Analyzing the Forces on the 10th Coin**:
- The 10th coin is at the bottom of the stack and has no coins above it.
- Therefore, the total force acting on the 10th coin is simply its own weight:
\[ F = mg \text{ (downward)} \]
- The statement claiming that the total force on the 10th coin is \( 9mg \) (downward) is incorrect because there are no coins above it to exert additional force.

### Conclusion:
The statement that is **not true** is that the total force on the 10th coin is \( 9mg \) in the downward direction.

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