In a practical unit if the unit of mass becomes double and that of unit of time becomes half, then 8 joule will be equal to _________ unit of work.

Options

A. 6
B. 4
C. 1
D. 10

Answer

To solve the problem, we need to analyze how the changes in the units of mass and time affect the value of 8 joules in the new unit system.

### Step-by-Step Solution:

1. **Understand the Current Units**:
- The SI unit of mass is kilograms (kg).
- The SI unit of time is seconds (s).
- The unit of work (or energy) is joules (J), which is defined as:
\[ 1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]

2. **Identify Changes in Units**:
- The unit of mass becomes double:
\[ \text{New unit of mass} = 2 \, \text{kg} \]
- The unit of time becomes half:
\[ \text{New unit of time} = \frac{1}{2} \, \text{s} \]

3. **Express Joules in Terms of New Units**:
- The original expression for joules is:
\[ 1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]
- In the new unit system, we replace the kg and s:
\[ 1 \, \text{J} = \frac{1 \, \text{kg}}{2} \cdot \text{m}^2 \left(\frac{1}{\frac{1}{2} \, \text{s}}\right)^2 \]

4. **Calculate the New Expression**:
- Substitute the new units into the expression:
\[ 1 \, \text{J} = \frac{1}{2} \, \text{kg} \cdot \text{m}^2 \cdot \left(2 \, \text{s}\right)^2 \]
- Simplifying this gives:
\[ 1 \, \text{J} = \frac{1}{2} \, \text{kg} \cdot \text{m}^2 \cdot 4 \, \text{s}^2 = 2 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]

5. **Relate 8 Joules to the New Unit**:
- Now, we can express 8 joules in terms of the new unit:
\[ 8 \, \text{J} = 8 \cdot 2 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 16 \, \text{new joules} \]
- Since 1 new joule is equivalent to 2 joules, we find:
\[ 8 \, \text{J} = 4 \, \text{new joules} \]

### Final Answer:
Thus, 8 joules will be equal to **4 new units of work**.