Question

A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

• A. 5 m/s
• B. 4 m/s
• C. 2 m/s
• D. 6 m/s

Answer 1

The Correct Option is A

To solve the problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces are acting on it.

Step-by-step Solution: 

1. Calculate the initial momentum of the body:

The initial mass of the body is \(1000 \, \text{kg}\) and its initial velocity is \(6 \, \text{m/s}\). Thus, the initial momentum (\(p_{\text{initial}}\)) is given by:

\(p_{\text{initial}} = m_{\text{initial}} \times v_{\text{initial}} = 1000 \times 6 = 6000 \, \text{kg m/s}\)

1. Calculate the final momentum of the system:

After adding 200 kg, the total mass becomes \(1000 + 200 = 1200 \, \text{kg}\). Let the final velocity be \(v_{\text{final}}\). The final momentum (\(p_{\text{final}}\)) is expressed as:

\(p_{\text{final}} = m_{\text{final}} \times v_{\text{final}} = 1200 \times v_{\text{final}}\)

1. Apply the conservation of momentum:

According to the conservation of momentum:

\(p_{\text{initial}} = p_{\text{final}}\)

\(6000 = 1200 \times v_{\text{final}}\)

1. Solve for \(v_{\text{final}}\):

Rearrange the equation for \(v_{\text{final}}\):

\(v_{\text{final}} = \frac{6000}{1200} = 5 \, \text{m/s}\)

Thus, the final velocity of the body after adding 200 kg extra mass is 5 m/s.

Conclusion: The correct answer is \(5 \, \text{m/s}\), which matches option

5 m/s

. This result confirms that option

5 m/s

is the correct choice.

 

Answer 2

Since there are no external forces, momentum is conserved. Initially:

\[ \text{Initial momentum} = 1000 \times 6 = 6000 \, \text{kg m/s} \]

After adding 200 kg of mass, the total mass becomes 1200 kg. Let the final velocity be \(v\).

Using conservation of momentum:

\[ 1200 \times v = 6000 \] \[ v = \frac{6000}{1200} = 5 \, \text{m/s} \]