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 one unit of power in the given system of units, we will follow these steps:

### Step 1: Understand the formula for power
Power (P) is defined as the work done (W) per unit of time (t). Mathematically, this is expressed as:
\[ P = \frac{W}{t} \]

### Step 2: Relate work done to force and displacement
Work done is defined as the product of force (F) and displacement (d):
\[ W = F \cdot d \]
And force is defined as mass (m) times acceleration (a):
\[ F = m \cdot a \]
Thus, we can express power as:
\[ P = \frac{F \cdot d}{t} = \frac{m \cdot a \cdot d}{t} \]

### Step 3: Identify the units in the given system
According to the problem:
- 1 unit of time = 5 seconds
- 1 unit of mass = 20 kg
- 1 unit of length = 10 m

### Step 4: Substitute the units into the power formula
We need to express acceleration (a) in terms of the given units. Acceleration is defined as:
\[ a = \frac{d}{t^2} \]
Using the units provided:
- Displacement (d) = 10 m (1 unit of length)
- Time (t) = 5 s (1 unit of time)

Thus, the acceleration in the given units can be calculated as:
\[ a = \frac{10 \, \text{m}}{(5 \, \text{s})^2} = \frac{10}{25} = 0.4 \, \text{m/s}^2 \]

### Step 5: Substitute the values into the power formula
Now we can substitute the values into the power equation:
\[ P = \frac{m \cdot a \cdot d}{t} \]
Substituting the known values:
\[ P = \frac{(20 \, \text{kg}) \cdot (0.4 \, \text{m/s}^2) \cdot (10 \, \text{m})}{5 \, \text{s}} \]

### Step 6: Calculate the power
Now we can compute the power:
\[ P = \frac{20 \cdot 0.4 \cdot 10}{5} \]
Calculating the numerator:
\[ 20 \cdot 0.4 = 8 \]
\[ 8 \cdot 10 = 80 \]
Now divide by the denominator:
\[ P = \frac{80}{5} = 16 \]

### Step 7: Conclusion
Thus, one unit of power in this system corresponds to:
\[ \text{1 unit of power} = 16 \, \text{W} \]