Two blocks of steel A and B, A being two times heavier than B, are at `40^@C`. The ratio of heat content of A to B is

Options

A. 1
B. 4
C. 2
D. `1/2`

Answer

To find the ratio of heat content of two blocks of steel A and B, we can follow these steps:

### Step 1: Define the Mass of Each Block
Let the mass of block B be \( m \). Since block A is two times heavier than block B, we can express the mass of block A as:
\[ \text{Mass of A} = 2m \]

### Step 2: Define the Specific Heat Capacity
Both blocks are made of steel, which means they have the same specific heat capacity. Let the specific heat capacity of both blocks be \( S \).

### Step 3: Calculate the Heat Content of Each Block
The heat content (or heat capacity) of an object can be calculated using the formula:
\[ \text{Heat Content} = \text{Mass} \times \text{Specific Heat Capacity} \times \text{Temperature} \]
Since both blocks are at the same temperature (\( 40^\circ C \)), we can ignore the temperature in the ratio calculation.

For block A, the heat content \( Q_A \) is:
\[ Q_A = \text{Mass of A} \times S = (2m) \times S = 2mS \]

For block B, the heat content \( Q_B \) is:
\[ Q_B = \text{Mass of B} \times S = m \times S = mS \]

### Step 4: Calculate the Ratio of Heat Content
Now, we can find the ratio of the heat content of block A to block B:
\[ \text{Ratio} = \frac{Q_A}{Q_B} = \frac{2mS}{mS} \]
When we simplify this, we find:
\[ \text{Ratio} = \frac{2mS}{mS} = 2 \]

### Conclusion
The ratio of the heat content of block A to block B is:
\[ \text{Ratio} = 2 \]