The volume change of a solid copper cube 10 cm on an edge, when subjected to a pressure of 7 MPa is
(Bulk modulus of copper 140 GPa)

Options

A. `5xx10^(-2) cm^(3)`
B. `10xx10^(-2) cm^(3)`
C. `15 xx 10^(-2) cm^(3)`
D. `8xx 10^(-1)cm^(3)`

Explanation

To find the volume change of a solid copper cube when subjected to a pressure, we can use the formula related to bulk modulus. Here’s a step-by-step solution:

### Step 1: Understand the Given Values
- Edge length of the cube (L) = 10 cm = \(10 \times 10^{-2}\) m
- Pressure (P) = 7 MPa = \(7 \times 10^6\) Pa
- Bulk modulus of copper (B) = 140 GPa = \(140 \times 10^9\) Pa

### Step 2: Calculate the Volume of the Cube
The volume (V) of the cube can be calculated using the formula for the volume of a cube:
\[ V = L^3 \]
Substituting the value of L:
\[ V = (10 \times 10^{-2})^3 = 10^3 \times (10^{-2})^3 = 1000 \times 10^{-6} = 1 \times 10^{-3} \, \text{m}^3 \]

### Step 3: Use the Bulk Modulus Formula
The bulk modulus (B) is defined as:
\[ B = -\frac{P}{\frac{\Delta V}{V}} \]
Rearranging the formula to find the change in volume (\(\Delta V\)):
\[ \Delta V = -\frac{P \cdot V}{B} \]

### Step 4: Substitute the Values into the Formula
Now we can substitute the known values into the equation:
\[ \Delta V = -\frac{(7 \times 10^6) \cdot (1 \times 10^{-3})}{140 \times 10^9} \]

### Step 5: Calculate \(\Delta V\)
Calculating the numerator:
\[ 7 \times 10^6 \times 1 \times 10^{-3} = 7 \times 10^3 = 7000 \]
Now substituting into the equation:
\[ \Delta V = -\frac{7000}{140 \times 10^9} \]
Calculating the denominator:
\[ 140 \times 10^9 = 140000000000 \]
Now, performing the division:
\[ \Delta V = -\frac{7000}{140000000000} = -5 \times 10^{-8} \, \text{m}^3 \]

### Final Answer
The volume change of the solid copper cube is:
\[ \Delta V = -5 \times 10^{-8} \, \text{m}^3 \]