The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :

Solution

Physics sir · 3 steps

Constant resistance means kinetic energy drops by equal amounts per cm, so compare energy, not speed.

1. Work-energy theorem. The resistive force F is constant, so the work it does is F × d. That work equals the kinetic energy lost. Equal distances therefore take away equal amounts of kinetic energy.
2. First 4 cm. Speed falls from v to v/3, so kinetic energy falls from K to K/9. The bullet loses 8/9K over these 4 cm and still has 1/9K left.

   x/4 = (1/9K)/(8/9K) = 1/8

3. So. x = 4/8 = 0.5 cm. The bullet stops after 4.5 cm in total, which is option (c).

The idea to keep. Under a constant force, kinetic energy changes in proportion to distance, and kinetic energy goes as v². Always convert a speed ratio into a kinetic energy ratio before scaling distances.

Answer from the NTA final answer key. Solution by PrepWiser.