The physical quantity that has no dimensions is

Options

A. Angular velocity
B. Linear momentum
C. Angular momentum
D. Strain

Answer

To solve the question regarding the physical quantity that has no dimensions, we can follow these steps:

### Step 1: Understand the Concept of Dimensionless Quantities
Dimensionless quantities are those that do not have any physical dimensions associated with them. This means that they do not depend on the fundamental quantities such as length, mass, time, etc.

**Hint:** Recall that dimensionless quantities are often ratios of similar quantities.

### Step 2: Identify Examples of Dimensionless Quantities
One common example of a dimensionless quantity is strain. Strain is defined as the ratio of change in length to the original length. Since both quantities (change in length and original length) have the same dimension (length), their ratio is dimensionless.

**Hint:** Think about other physical quantities that are ratios of similar types of measurements.

### Step 3: Define Strain
Strain (ε) is mathematically defined as:
\[ \text{Strain} = \frac{\text{Change in Length}}{\text{Original Length}} \]
Since both the numerator and denominator have the same dimensions (length), the dimensions cancel out, making strain a dimensionless quantity.

**Hint:** Consider how ratios work in terms of dimensions.

### Step 4: Conclude the Answer
Since strain is a well-known example of a dimensionless quantity, we can conclude that the physical quantity that has no dimensions is strain.

**Final Answer:** The physical quantity that has no dimensions is strain.