question_answer

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?                            [AIEEE 2005]

A) 3.0 cm

B) 2.0 cm

C) 1.5 cm

D) 1.0 cm

Correct Answer: D

Solution :

[d] According to work-energy theorem,

Case I When bullet is penetrating 3 cm

where, F is resistive force and  is initial speed.

Case II Let the further distance travelled by the bullet before coming to rest is s.

\[-F(3+s)\,={{K}_{f}}-{{K}_{i}}=-\frac{1}{2}\,mv_{0}^{2}\]

or

or

or