A packet contains silver powder of mass 20.23 g `pm` 0.01 g Some of the powder of mass 5.75 g `pm` 0.01 g is taken out from it The mass of the powder lell back is

Options

A. `14.48 g pm 0.00 g`
B. `14.48 pm 0.02 g`
C. `14.5 g pm 0.1 g `
D. `14.5 g pm 0.2 g`

Answer

To solve the problem of finding the mass of silver powder remaining after taking some out, we can follow these steps:

### Step 1: Identify the given values
- The mass of the silver powder in the packet (X) is 20.23 g with an uncertainty of ±0.01 g.
- The mass of the silver powder taken out (Y) is 5.75 g with an uncertainty of ±0.01 g.

### Step 2: Write the formula for the remaining mass
The mass of the powder remaining (Z) can be calculated using the formula:
\[ Z = X - Y \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ Z = (20.23 \, \text{g} \pm 0.01 \, \text{g}) - (5.75 \, \text{g} \pm 0.01 \, \text{g}) \]

### Step 4: Calculate the true value of the remaining mass
Now, calculate the true value:
\[ Z = 20.23 \, \text{g} - 5.75 \, \text{g} = 14.48 \, \text{g} \]

### Step 5: Calculate the uncertainty in the remaining mass
When subtracting values, the uncertainties add up. Therefore, the uncertainty in Z is:
\[ \text{Uncertainty in } Z = 0.01 \, \text{g} + 0.01 \, \text{g} = 0.02 \, \text{g} \]

### Step 6: Write the final result
The final result for the mass of the silver powder remaining is:
\[ Z = 14.48 \, \text{g} \pm 0.02 \, \text{g} \]

### Step 7: Conclusion
Thus, the mass of the silver powder remaining after taking out some is:
\[ \text{Final Answer: } 14.48 \, \text{g} \pm 0.02 \, \text{g} \]

---