State which of the following statements are true.

Options

A. Mechanical advantage is always a unitless quantity
B. Velocity ratio is also called displacement ratio
C. Efficiency is always less than one
D. both 1 and 2

Explanation

To solve the question regarding which statements are true, let's analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement:** Mechanical advantage is always a unitless quantity.

**Explanation:**
Mechanical advantage (MA) is defined as the ratio of load (output force) to effort (input force). Mathematically, it is expressed as:

\[ MA = \frac{\text{Load}}{\text{Effort}} \]

Since both load and effort are measured in the same unit (force), when you divide one by the other, the units cancel out. Therefore, mechanical advantage is indeed a unitless quantity.

**Conclusion:** Statement 1 is **True**.

### Step 2: Analyze Statement 2
**Statement:** Velocity ratio is also known as displacement ratio.

**Explanation:**
Velocity ratio (VR) is defined as the ratio of the velocities of the input and output. It can be expressed as:

\[ VR = \frac{\text{Velocity}_1}{\text{Velocity}_2} \]

Velocity can be defined in terms of displacement over time:

\[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \]

Thus, substituting the definitions of velocity into the VR formula gives:

\[ VR = \frac{\frac{D_1}{T}}{\frac{D_2}{T}} = \frac{D_1}{D_2} \]

The time cancels out, showing that the velocity ratio is indeed equivalent to the displacement ratio.

**Conclusion:** Statement 2 is **True**.

### Step 3: Analyze Statement 3
**Statement:** Efficiency is always less than one.

**Explanation:**
Efficiency (η) is defined as the ratio of useful work output to the total work input, expressed as:

\[ \eta = \frac{\text{Useful Work Output}}{\text{Total Work Input}} \]

In real machines, efficiency is typically less than one due to losses (like friction). However, for an ideal machine, the efficiency can be equal to one (100% efficiency), meaning all input work is converted to useful output work without any losses.

**Conclusion:** Statement 3 is **False**.

### Final Conclusion
Based on the analysis:
- Statement 1 is **True**.
- Statement 2 is **True**.
- Statement 3 is **False**.

Thus, the correct options are Statements 1 and 2.