Question

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :

• A. 0.32
• B. 0.44
• C. 0.16
• D. 0.84

Answer 1

The Correct Option is D

The initial kinetic energy of the bullet is:

\[ K_i = \frac{1}{2} m (100)^2 \]

The final kinetic energy of the bullet is:

\[ K_f = \frac{1}{2} m (40)^2 \]

The percentage loss in kinetic energy is given by:

\[ \% \text{loss} = \frac{|K_f - K_i|}{K_i} \times 100 \]

Substituting the expressions for \( K_i \) and \( K_f \):

\[ \% \text{loss} = \frac{\left| \frac{1}{2} m (40)^2 - \frac{1}{2} m (100)^2 \right|}{\frac{1}{2} m (100)^2} \times 100 \]

Simplify:

\[ \% \text{loss} = \frac{|1600 - 10000|}{10000} \times 100 \]

\[ \% \text{loss} = \frac{8400}{10000} \times 100 = 84\% \]

Final Answer: 84% (Option 4)