A 2m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians the shear strain developed will be

Options

A. 0.002
B. 0.004
C. 0.008
D. 0.016

Answer

To find the shear strain developed in the rod when it is twisted, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the rod (L) = 2 m
- Radius of the rod (r) = 1 cm = 0.01 m (conversion from cm to m)
- Twist (θ) = 0.8 radians

2. **Calculate the deformation (Δx):**
The deformation caused by the twist can be calculated using the formula:
\[ \Delta x = r \cdot \theta \]
Substituting the values:
\[ \Delta x = 0.01 \, \text{m} \cdot 0.8 = 0.008 \, \text{m} \]

3. **Calculate the shear strain (γ):**
The shear strain is defined as the ratio of the deformation to the length of the rod:
\[ \gamma = \frac{\Delta x}{L} \]
Substituting the values:
\[ \gamma = \frac{0.008 \, \text{m}}{2 \, \text{m}} = 0.004 \]

4. **Final answer:**
The shear strain developed in the rod is:
\[ \gamma = 0.004 \]