A bullet is fired into a fixed target looses one third of its velocity after travelling 4 cm. It penetrates further D × 10⁻³ m before coming to rest. The value of D is :

Solution

Physics sir · 4 steps

The resisting force is constant, so each distance is proportional to the kinetic energy it removes.

1. Set up energies. Losing one third of its velocity means the speed drops from v to 2v/3. Call the starting kinetic energy K = 1/2mv². After 4 cm the kinetic energy is 4/9K, so 5/9K has been lost.
2. Work-energy theorem. The target pushes back on the bullet with a constant force F. The work done against F equals the kinetic energy lost. For the first 4 cm this gives F × 4 cm = 5/9K.
3. Remaining distance. The bullet stops once its remaining 4/9K is used up over a further distance x, so F × x = 4/9K. Divide this equation by the first one.

   x/(4 cm) = (4/9K)/(5/9K) = 4/5

4. So. x = 4/5 × 4 cm = 3.2 cm = 32 × 10⁻³ m, so D = 32, which is option (b).

The idea to keep. Under a constant resisting force, the distance travelled is proportional to the kinetic energy lost. Compare energies, not speeds, because kinetic energy goes as v².

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