A metallic cube of side 10 cm is subjected to a shearing force of 300 kgf. The top force is displaced through 0.25 cm with respect ot the bottom ? Calculate the shearing strain produced .

Options

A. 0.25
B. 2.5
C. 0.025
D. 0.08

Explanation

To calculate the shearing strain produced in the metallic cube, we can follow these steps:

### Step 1: Understand the given data
- Side length of the cube (L) = 10 cm
- Shearing force = 300 kgf (not needed for calculating shearing strain)
- Displacement of the top face (ΔL) = 0.25 cm

### Step 2: Convert the displacement into meters
Since we want to maintain consistency in units, we convert the displacement from centimeters to meters.
- ΔL = 0.25 cm = 0.25 × 10^-2 m = 0.0025 m

### Step 3: Calculate the original length in meters
Convert the side length of the cube from centimeters to meters.
- L = 10 cm = 10 × 10^-2 m = 0.1 m

### Step 4: Use the formula for shearing strain
The formula for shearing strain (γ) is given by:
\[ \text{Shearing Strain} (\gamma) = \frac{\Delta L}{L} \]

### Step 5: Substitute the values into the formula
Now, substitute the values of ΔL and L into the formula:
\[ \gamma = \frac{0.0025 \, \text{m}}{0.1 \, \text{m}} \]

### Step 6: Calculate the shearing strain
Perform the calculation:
\[ \gamma = \frac{0.0025}{0.1} = 0.025 \]

### Final Answer
The shearing strain produced is **0.025**.

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