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 solve the problem, we need to calculate the shearing strain produced in the metallic cube when a shearing force is applied. Here are the steps to find the solution:

### Step 1: Understand the Given Information
- The side length of the metallic cube is 10 cm.
- The shearing force applied is 300 kgf.
- The displacement (or change in length) of the top face with respect to the bottom is 0.25 cm.

### Step 2: Convert Units
Since we need to calculate the shearing strain, we should convert the displacement from centimeters to meters for consistency in SI units.
- Displacement (ΔL) = 0.25 cm = 0.25 × 10^(-2) m = 0.0025 m.

### Step 3: Calculate the Original Length (L)
The original length (L) for the shearing strain calculation is the side length of the cube, which is given as 10 cm.
- Convert this to meters:
- L = 10 cm = 10 × 10^(-2) m = 0.1 m.

### Step 4: Calculate the Shearing Strain (γ)
The shearing strain (γ) is defined as the ratio of the displacement (ΔL) to the original length (L).
- Formula:
\[ \text{Shearing Strain} (\gamma) = \frac{\Delta L}{L} \]
- Substitute the values:
\[ \gamma = \frac{0.0025 \, \text{m}}{0.1 \, \text{m}} = 0.025 \]

### Step 5: Conclusion
The shearing strain produced in the metallic cube is 0.025.

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