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 `6^(th)` coin due to `7^(th)` coin is 4mg (downwards)
B. The force on the `6^(th)` coin 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 solve the problem, we need to analyze the forces acting on the coins stacked on top of each other. We have 10 one-rupee coins, each with a mass \( m \).

### Step-by-step Solution:

1. **Understanding the Setup:**
- We have 10 coins stacked vertically on a table.
- Each coin has a mass \( m \).

2. **Identifying the Forces:**
- The force acting on each coin is due to the weight of the coins above it.
- The weight of a single coin is given by \( mg \), where \( g \) is the acceleration due to gravity.

3. **Calculating the Force on the 6th Coin:**
- The 6th coin has 4 coins above it (7th, 8th, 9th, and 10th).
- The total mass above the 6th coin is \( 4m \).
- Therefore, the force acting downward on the 6th coin due to the coins above it is:
\[ F = \text{mass above} \times g = 4m \cdot g = 4mg \]

4. **Applying Newton's Third Law:**
- According to Newton's third law, the force exerted by the 6th coin on the 7th coin will be equal in magnitude and opposite in direction to the force exerted on the 6th coin by the 7th coin.
- Thus, the force on the 6th coin due to the 7th coin is also \( 4mg \).

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, which is \( mg \).

6. **Identifying the False Statement:**
- Now we can evaluate the statements given in the question:
- The force on the 6th coin due to the 7th coin is \( 4mg \) (True).
- The reaction force of the 6th coin on the 7th coin is also \( 4mg \) (True).
- The total force on the 10th coin is \( 0 \) (False, as it has a weight of \( mg \)).
- Therefore, the statement that is NOT true is the one regarding the total force on the 10th coin.

### Conclusion:
The false statement is that the total force on the 10th coin is zero.