On a faulty balance if an object is kept on both scales consecutively then their weights are read as 6.4 g and 10 g. Find the true weight of that object.

Options

A. 10 g
B. 14 g
C. `8.2 g`
D. 8 g

Explanation

To find the true weight of the object using the readings from a faulty balance, we can follow these steps:

### Step 1: Identify the given weights
We have two readings from the faulty balance:
- \( W_1 = 6.4 \, \text{g} \)
- \( W_2 = 10 \, \text{g} \)

### Step 2: Use the formula for true weight
The formula to calculate the true weight \( W \) of the object when using two readings from a faulty balance is given by:
\[ W = \sqrt{W_1 \times W_2} \]

### Step 3: Substitute the values into the formula
Now, we substitute the values of \( W_1 \) and \( W_2 \) into the formula:
\[ W = \sqrt{6.4 \, \text{g} \times 10 \, \text{g}} \]

### Step 4: Calculate the product
First, calculate the product:
\[ 6.4 \times 10 = 64 \, \text{g}^2 \]

### Step 5: Take the square root
Now, take the square root of the product:
\[ W = \sqrt{64 \, \text{g}^2} = 8 \, \text{g} \]

### Step 6: State the true weight
Thus, the true weight of the object is:
\[ W = 8 \, \text{g} \]

### Final Answer
The true weight of the object is **8 g**.

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