In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and 1 uint of length is 10m. In this system, one unit of power will correspond to :-

Options

A. 16 watts
B. `(1)/(16)` watts
C. 25 watts
D. none of these.

Answer

To find the unit of power in the given system of units, we need to follow these steps:

1. **Identify the given units in the new system:**
- 1 unit of time = 5 seconds
- 1 unit of mass = 20 kg
- 1 unit of length = 10 meters

2. **Recall the formula for power:**
\[ \text{Power} = \frac{\text{Work done}}{\text{Time}} \]
Work done (W) is given by:
\[ W = \text{Force} \times \text{Displacement} \]
Force (F) is given by:
\[ F = \text{Mass} \times \text{Acceleration} \]

3. **Substitute the expressions into the power formula:**
\[ \text{Power} = \frac{\text{Mass} \times \text{Acceleration} \times \text{Displacement}}{\text{Time}} \]

4. **Convert each quantity to the given units:**
- Mass: 1 unit of mass = 20 kg
- Acceleration: \(\text{Acceleration} = \frac{\text{Length}}{\text{Time}^2}\)
\[ \text{Acceleration} = \frac{10 \text{ meters}}{(5 \text{ seconds})^2} = \frac{10}{25} \text{ m/s}^2 = 0.4 \text{ m/s}^2 \]
- Displacement: 1 unit of length = 10 meters
- Time: 1 unit of time = 5 seconds

5. **Substitute these values into the power formula:**
\[ \text{Power} = \frac{20 \text{ kg} \times 0.4 \text{ m/s}^2 \times 10 \text{ meters}}{5 \text{ seconds}} \]

6. **Calculate the power:**
\[ \text{Power} = \frac{20 \times 0.4 \times 10}{5} \text{ watts} \]
Simplify the expression:
\[ \text{Power} = \frac{80}{5} \text{ watts} = 16 \text{ watts} \]

Therefore, one unit of power in the given system of units corresponds to 16 watts.