A metallic cube whose each side is 10 cm is subjected to a shearing force of 100 kgf. Calculate the shearing produced.

Options

A. `9.8xx10^(4)Nm^(-2)`
B. `10 Nm^(-2)`
C. `9.8 Nm^(-2)`
D. `9.8xx10^(2) Nm^(-2)`

Explanation

To solve the problem of calculating the shearing produced in a metallic cube subjected to a shearing force, we will follow these steps:

### Step 1: Understand the Given Data
- The side length of the metallic cube (L) = 10 cm = 0.1 m (conversion from cm to m)
- The shearing force (F) = 100 kgf

### Step 2: Convert the Shearing Force to Newtons
1 kgf (kilogram-force) is equivalent to 9.8 N (newtons). Therefore, we convert the shearing force:
\[ F = 100 \, \text{kgf} \times 9.8 \, \text{N/kgf} = 980 \, \text{N} \]

### Step 3: Calculate the Area of One Face of the Cube
The area (A) of one face of the cube can be calculated using the formula:
\[ A = L^2 \]
Substituting the value of L:
\[ A = (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2 \]

### Step 4: Calculate the Shearing Stress
Shearing stress (\(\tau\)) is defined as the force (F) applied per unit area (A):
\[ \tau = \frac{F}{A} \]
Substituting the values:
\[ \tau = \frac{980 \, \text{N}}{0.01 \, \text{m}^2} = 98000 \, \text{N/m}^2 = 98 \, \text{kPa} \]

### Step 5: Calculate the Shearing Produced
To find the shearing produced (which is often represented as the shear strain), we can use the relationship between shear stress and shear modulus (G):
\[ \text{Shearing produced} = \frac{\tau}{G} \]
However, since we do not have the value of the shear modulus (G) for the metallic cube, we will stop at the shearing stress calculation.

### Final Result
The shearing stress produced in the metallic cube is:
\[ \tau = 98000 \, \text{N/m}^2 \text{ or } 98 \, \text{kPa} \]