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 fundamentally related. We can calculate kinetic energy directly from momentum and mass without needing to calculate velocity first.
Step 2: Key Formula or Approach:
The relationship between kinetic energy (\(K\)) and momentum (\(p\)) is:
\[ K = \frac{p^2}{2m} \] Step 3: Detailed Explanation:
Given values:
Mass \(m = 5\) kg
Momentum \(p = 4 \text{ kg ms}^{-1}\)
Substitute these directly into the relationship formula:
\[ K = \frac{(4)^2}{2 \times 5} \] \[ K = \frac{16}{10} \] \[ K = 1.6 \text{ J} \] Step 4: Final Answer:
The kinetic energy is 1.6 J.