Question

Momentum of a body is increased to three times its original value. By what percentage will its kinetic energy change?

• A. \(300\%\)
• B. \(900\%\)
• C. \(200\%\)
• D. \(800\%\)

Hint:

Kinetic energy is proportional to square of momentum: \(K \propto p^2\). Always square the factor of change in momentum.

Answer 1

The Correct Option is D

Step 1: Write relation between kinetic energy and momentum.
Kinetic energy in terms of momentum is:
\[ K = \frac{p^2}{2m} \]

Step 2: Analyze change in momentum.
Given final momentum:
\[ p' = 3p \]

Step 3: Find new kinetic energy.
\[ K' = \frac{(3p)^2}{2m} \]
\[ K' = \frac{9p^2}{2m} \]
\[ K' = 9K \]

Step 4: Calculate increase in kinetic energy.
\[ \Delta K = K' - K = 9K - K = 8K \]

Step 5: Find percentage change.
\[ \text{Percentage increase} = \frac{8K}{K} \times 100 \]
\[ = 800\% \]

Step 6: Interpretation.
Kinetic energy increases as square of momentum, hence tripling momentum increases KE nine times.

Step 7: Final answer.
\[ \boxed{800\%} \]