Question

The kinetic energy of a body of mass $5 \text{ kg}$ having a linear momentum $4 \text{ kg ms}^{-1}$ is

• A. $2.6 \text{ J}$
• B. $1.6 \text{ J}$
• C. $1.5 \text{ J}$
• D. $2.5 \text{ J}$
• E. $3.6 \text{ J}$

Hint:

Remembering \( K = \frac{p^2}{2m} \) is much faster than first calculating velocity \( v = p/m \) and then using \( \frac{1}{2}mv^2 \).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Kinetic energy and linear momentum are both related to the motion of an object. There is a direct mathematical relationship between them involving the mass of the object.
Key Formula or Approach:
Kinetic Energy (\( K \)) in terms of momentum (\( p \)) and mass (\( m \)) is:
\[ K = \frac{p^2}{2m} \]

Step 2: Detailed Explanation:
Given:
Mass \( m = 5 \text{ kg} \)
Momentum \( p = 4 \text{ kg ms}^{-1} \)
Applying the formula:
\[ K = \frac{4^2}{2 \times 5} \]
\[ K = \frac{16}{10} \]
\[ K = 1.6 \text{ J} \]

Step 3: Final Answer:
The kinetic energy of the body is $1.6 \text{ J}$.