Question

The kinetic energy of a particle is 10000 joule with the mass 2kg. Find the momentum for the particle?

• A. 200 kg m/s
• B. 400 kg m/s
• C. 800 kg m/s
• D. 600 kg m/s

Answer 1

The Correct Option is A

To find the momentum of a particle given its kinetic energy and mass, we can use the relationship between kinetic energy and momentum. The kinetic energy \( KE \) of a particle is given by:

\(KE = \frac{1}{2} m v^2\)

where \( m \) is the mass of the particle and \( v \) is its velocity.

The momentum \( p \) of a particle is given by:

\(p = mv\)

Let's start by solving for \( v \) using the formula for kinetic energy. Rearrange the kinetic energy formula to solve for velocity \( v \):

\(v = \sqrt{\frac{2 \times KE}{m}}\)

Plug in the given values: \( KE = 10000 \, \text{J} \) and \( m = 2 \, \text{kg} \).

\(v = \sqrt{\frac{2 \times 10000}{2}}\)

\(v = \sqrt{\frac{20000}{2}}\)

\(v = \sqrt{10000}\)

\(v = 100 \, \text{m/s}\)

Now, use the momentum formula to find the momentum \( p \):

\(p = mv\)

Substitute the known values:

\(p = 2 \times 100\)

\(p = 200 \, \text{kg m/s}\)

Therefore, the momentum of the particle is 200 kg m/s.