Which of the statements are false?

Options

A. Physical quantity represented by volume is `dm^(3)`
B. The length of pencil is `5 "cms"`.
C. The work done by a system is 5 Joules.
D. Air sometimes is considered as a hetrogeneous mixture due to the presence of dust particles which form a separate phase.

Explanation

To determine which statements are false, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement:** "Physical quantity is represented by volume is decimeter cube."

**Analysis:**
- The unit of volume can indeed be represented in decimeter cube (dm³).
- Other units for volume include liter (L) and milliliter (mL), and 1 liter is equal to 1 decimeter cube.

**Conclusion:** This statement is **true**.

### Step 2: Analyze the second statement
**Statement:** "The length of pencil is 5 centimeters."

**Analysis:**
- The unit of length is correctly stated as centimeters (cm).
- However, the plural form "centimeters" is not typically used in scientific writing when specifying a measurement. The correct form should be "5 cm" or "the length of the pencil is 5 centimeter."

**Conclusion:** This statement is **false** due to the incorrect use of the plural form.

### Step 3: Analyze the third statement
**Statement:** "The work done by a system is 5 joules."

**Analysis:**
- The unit of work is Joule (J), and it is customary to use the singular form when stating a specific amount of work done.
- The correct way to phrase this would be "5 joules" when referring to the unit in general, but in the context of a specific measurement, it should be "5 J."

**Conclusion:** This statement is **false** due to the incorrect use of the plural form.

### Step 4: Analyze the fourth statement
**Statement:** "Air sometimes is considered as a heterogeneous mixture due to the presence of dashed particles which form a separate phase."

**Analysis:**
- Air is generally a homogeneous mixture of gases. However, in certain conditions (e.g., when dust or other particles are present), it can be considered a heterogeneous mixture.
- The presence of particles can indeed create a separate phase, making this statement accurate.

**Conclusion:** This statement is **true**.

### Final Conclusion
The false statements are:
1. "The length of pencil is 5 centimeters." (Incorrect plural form)
2. "The work done by a system is 5 joules." (Incorrect plural form)