The linear momentum of a particle of mass 1kg and kinetic energy 2J is equal to

Options

A. `2kg -ms^(-1)`
B. `4 kg -ms^(-1)`
C. `sqrt2 kg -ms^(-1)`
D. `4 sqrt2 kg -ms^(-1)`

Explanation

To find the linear momentum of a particle with a mass of 1 kg and a kinetic energy of 2 J, we can follow these steps:

### Step 1: Write down the formula for kinetic energy.
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity.

### Step 2: Substitute the known values into the kinetic energy formula.
We know the kinetic energy is 2 J and the mass is 1 kg. Substituting these values into the formula gives:
\[ 2 = \frac{1}{2} \times 1 \times v^2 \]

### Step 3: Solve for \( v^2 \).
To isolate \( v^2 \), we can rearrange the equation:
\[ 2 = \frac{1}{2} v^2 \implies v^2 = 2 \times 2 = 4 \]

### Step 4: Find \( v \) by taking the square root of \( v^2 \).
Taking the square root of both sides, we get:
\[ v = \sqrt{4} = 2 \, \text{m/s} \]

### Step 5: Write down the formula for momentum.
The formula for momentum (P) is given by:
\[ P = mv \]

### Step 6: Substitute the values of mass and velocity into the momentum formula.
Now, substituting the mass (1 kg) and the velocity (2 m/s) into the momentum formula gives:
\[ P = 1 \times 2 = 2 \, \text{kg m/s} \]

### Conclusion:
The linear momentum of the particle is \( 2 \, \text{kg m/s} \).

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