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 understand how the changes in the units of mass and time affect the unit of work, which is measured in joules.

### Step-by-Step Solution:

1. **Understanding the Unit of Work**:
The unit of work (joule) is defined as:
\[ 1 \text{ Joule} = 1 \text{ kg} \cdot \text{m} \cdot \text{s}^{-2} \]
Therefore, \(8 \text{ Joules} = 8 \text{ kg} \cdot \text{m} \cdot \text{s}^{-2}\).

2. **Changes in Units**:
- The new unit of mass \(kg'\) is double the original unit:
\[ kg' = 2 \cdot kg \]
- The new unit of time \(s'\) is half the original unit:
\[ s' = \frac{1}{2} \cdot s \]

3. **Substituting New Units into the Work Formula**:
We need to express the work in terms of the new units. The work in joules can be rewritten using the new units:
\[ W = kg' \cdot m \cdot (s')^{-2} \]
Substituting the new units into this equation:
\[ W = (2 \cdot kg) \cdot m \cdot \left(\frac{1}{2} s\right)^{-2} \]

4. **Calculating the New Time Unit**:
\[ (s')^{-2} = \left(\frac{1}{2} s\right)^{-2} = \frac{1}{\left(\frac{1}{2}\right)^2 s^2} = \frac{4}{s^2} \]

5. **Putting it All Together**:
Now substituting this back into the work equation:
\[ W = (2 \cdot kg) \cdot m \cdot \frac{4}{s^2} \]
Simplifying this gives:
\[ W = \frac{8 \cdot kg \cdot m}{s^2} \]

6. **Comparing with Original Work**:
We know that \(8 \text{ Joules} = 8 \cdot kg \cdot m \cdot s^{-2}\). Thus, in the new units:
\[ W = 8 \cdot kg' \cdot m \cdot (s')^{-2} = 8 \text{ Joules} \]
Therefore, in the new unit of work, \(8 \text{ Joules}\) is equivalent to:
\[ 1 \text{ unit of work} \]

### Final Answer:
Thus, \(8 \text{ Joules}\) will be equal to **1 unit of work** in the new unit system.