A glass thermometer is unmarked and has length of colum `L_(100^(@))=60 cm L_(0^(@))=10 cm.` If L=50 cm, then temperature thermometer will be :-

Options

A. `70^(@)C`
B. `80^(@)C`
C. `90^(@)C`
D. `100^(@)C`

Answer

To solve the problem, we will use the formula for the temperature reading on an unmarked thermometer based on the lengths of the mercury column at different temperatures. The formula is given by:

\[ \theta = \frac{L - L_0}{L_{100} - L_0} \times 100 \]

Where:
- \( \theta \) is the temperature in degrees Celsius.
- \( L \) is the length of the mercury column at the unknown temperature.
- \( L_0 \) is the length of the mercury column at 0°C.
- \( L_{100} \) is the length of the mercury column at 100°C.

### Step-by-step Solution:

1. **Identify the given values:**
- \( L_{100} = 60 \, \text{cm} \)
- \( L_0 = 10 \, \text{cm} \)
- \( L = 50 \, \text{cm} \)

2. **Substitute the values into the formula:**
\[ \theta = \frac{L - L_0}{L_{100} - L_0} \times 100 \]
\[ \theta = \frac{50 \, \text{cm} - 10 \, \text{cm}}{60 \, \text{cm} - 10 \, \text{cm}} \times 100 \]

3. **Calculate the numerator and denominator:**
- Numerator: \( 50 \, \text{cm} - 10 \, \text{cm} = 40 \, \text{cm} \)
- Denominator: \( 60 \, \text{cm} - 10 \, \text{cm} = 50 \, \text{cm} \)

4. **Plug in the values:**
\[ \theta = \frac{40 \, \text{cm}}{50 \, \text{cm}} \times 100 \]

5. **Calculate the fraction:**
\[ \frac{40}{50} = 0.8 \]

6. **Multiply by 100 to find the temperature:**
\[ \theta = 0.8 \times 100 = 80 \, \text{°C} \]

### Final Answer:
The temperature indicated by the thermometer is \( \theta = 80 \, \text{°C} \).

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