The mass of a beaker is `(10.1 pm 0.1)`g when empty and `(17.3pm0.1)`g when filled with a liquid. The mass of the liquid with possible limits of accuracy is

Options

A. `(7.2pm 0.2 ) g`
B. `(7.2pm 0.1 )` g
C. `(7.1pm0.2 )g`
D. `(7.2pm 0.3)g`

Answer

To find the mass of the liquid and its possible limits of accuracy, we can follow these steps:

### Step 1: Identify the given values
- Mass of the empty beaker, \( m_1 = 10.1 \, \text{g} \) with an uncertainty of \( \Delta m_1 = 0.1 \, \text{g} \)
- Mass of the beaker filled with liquid, \( m_2 = 17.3 \, \text{g} \) with an uncertainty of \( \Delta m_2 = 0.1 \, \text{g} \)

### Step 2: Calculate the mass of the liquid
The mass of the liquid can be calculated using the formula:
\[ m_{\text{liquid}} = m_2 - m_1 \]
Substituting the values:
\[ m_{\text{liquid}} = 17.3 \, \text{g} - 10.1 \, \text{g} = 7.2 \, \text{g} \]

### Step 3: Calculate the uncertainty in the mass of the liquid
To find the uncertainty in the mass of the liquid, we need to consider the uncertainties in both measurements. The formula for the uncertainty in subtraction is:
\[ \Delta m_{\text{liquid}} = \Delta m_1 + \Delta m_2 \]
Substituting the uncertainties:
\[ \Delta m_{\text{liquid}} = 0.1 \, \text{g} + 0.1 \, \text{g} = 0.2 \, \text{g} \]

### Step 4: Write the final result
The mass of the liquid with its uncertainty is:
\[ m_{\text{liquid}} = 7.2 \pm 0.2 \, \text{g} \]

### Step 5: Conclusion
The possible limits of accuracy for the mass of the liquid are \( 7.2 \pm 0.2 \, \text{g} \).

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