If the unit of force is 1N, the unit of work done is 10 J and the unit of time is 1 second, the unit of mass is

Options

A. 10 kg
B. 1 kg
C. 0.1 kg
D. 100 kg

Answer

To find the unit of mass given the unit of force, work done, and time, we can follow these steps:

### Step 1: Understand the relationships between work, force, and mass
We know that:
- Work done (W) is given by the formula:
\[ W = F \times d \]
where \( F \) is the force and \( d \) is the displacement.

- Force (F) is defined as:
\[ F = m \times a \]
where \( m \) is the mass and \( a \) is the acceleration.

### Step 2: Substitute known values into the work formula
From the problem, we know:
- \( W = 10 \, \text{J} \) (joules)
- \( F = 1 \, \text{N} \) (newton)

Using the work formula:
\[ 10 \, \text{J} = 1 \, \text{N} \times d \]
This implies:
\[ d = \frac{10 \, \text{J}}{1 \, \text{N}} = 10 \, \text{m} \]

### Step 3: Use the force formula to find mass
Now we substitute the known values into the force formula. We know:
- \( F = 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \)

Using the formula \( F = m \times a \), we can express acceleration \( a \) in terms of displacement and time:
\[ a = \frac{d}{t^2} \]
Substituting \( d = 10 \, \text{m} \) and \( t = 1 \, \text{s} \):
\[ a = \frac{10 \, \text{m}}{(1 \, \text{s})^2} = 10 \, \text{m/s}^2 \]

### Step 4: Substitute acceleration back into the force equation
Now, substituting \( a \) back into the force equation:
\[ 1 \, \text{N} = m \times 10 \, \text{m/s}^2 \]
Rearranging gives:
\[ m = \frac{1 \, \text{N}}{10 \, \text{m/s}^2} \]

### Step 5: Calculate the mass
Since \( 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \):
\[ m = \frac{1 \, \text{kg} \cdot \text{m/s}^2}{10 \, \text{m/s}^2} = \frac{1 \, \text{kg}}{10} = 0.1 \, \text{kg} \]

### Conclusion
Thus, the unit of mass is:
\[ \text{Mass} = 0.1 \, \text{kg} \]

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