Ten coins are arranged one above the other. The mass of each coin is 10 g. Reaction force of the sixth coin from the bottom of the seventh coin is

Options

A. 0.392 N
B. 0.49 N
C. 0.98 N
D. 0.784 N

Answer

To find the reaction force of the sixth coin from the bottom of the seventh coin, we can follow these steps:

### Step 1: Understand the Arrangement of Coins
We have 10 coins stacked one above the other. Each coin has a mass of 10 grams.

### Step 2: Identify the Coins Involved
We need to find the reaction force on the sixth coin due to the seventh coin. The sixth coin is the one we are focusing on, and the seventh coin is the one exerting the force on it.

### Step 3: Determine the Weight of the Coins Below the Sixth Coin
The reaction force on the sixth coin from the seventh coin will be equal to the weight of the coins that are below the sixth coin. The coins below the sixth coin are the seventh, eighth, ninth, and tenth coins. Therefore, there are 4 coins below the sixth coin.

### Step 4: Calculate the Total Mass of the Coins Below
Each coin has a mass of 10 grams. Thus, the total mass of the four coins below the sixth coin is:
\[ \text{Total Mass} = 4 \times 10 \, \text{grams} = 40 \, \text{grams} \]

### Step 5: Convert Mass to Kilograms
Since we need to use SI units, we convert grams to kilograms:
\[ 40 \, \text{grams} = 40 \times 10^{-3} \, \text{kg} = 0.04 \, \text{kg} \]

### Step 6: Calculate the Weight of the Coins
The weight (W) of an object is given by the formula:
\[ W = m \times g \]
where \( m \) is the mass in kilograms and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Substituting the values:
\[ W = 0.04 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 0.392 \, \text{N} \]

### Step 7: Conclusion
The reaction force of the sixth coin from the bottom of the seventh coin is:
\[ \text{Reaction Force} = 0.392 \, \text{N} \]

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