Question

The linear momentum is increased by 50%, the kinetic energy will increase by

• A. 50%
• B. 100%
• C. 125%
• D. 25%

Hint:

\(KE \propto p^2\). If \(p\) increases by 50%, \(KE\) becomes \((1.5)^2 = 2.25\) times, i.e., increases by 125%.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
\(KE = \dfrac{p^2}{2m} \propto p^2\).
Step 2: Detailed Explanation:
New \(p' = 1.5p\)
New \(KE' = \dfrac{(1.5p)^2}{2m} = 2.25 \times \dfrac{p^2}{2m} = 2.25 \times KE\)
Increase \(= (2.25 - 1) \times 100% = 125%\)
Step 3: Final Answer:
KE increases by 125%.