question_answer

A 30 g bullet initially travelling at 120 m/s penetrates 12 cm into wooden block. The average resistance exerted by the wooden block is :

A)  1800 N        

B)  2000 N

C)  2200 N        

D)  2850 N

Correct Answer: A

Solution :

Key Idea: The bullet comes to rest inside the block, hence final velocity is zero. Let m be mass of bullet, travelling with initial velocity of 120 m/s (u). It comes to rest after travelling a distance of (0.12 m = 5) inside the block. Since, it comes to rest the final velocity (y) is zero. From equation of motion, we have                 \[{{v}^{2}}={{u}^{2}}+2\,as\] Here,     \[v=0,\,u=120\,m/s,\,s=0.12\,m\] \[\Rightarrow \] \[a=-\frac{{{u}^{2}}}{2\,s}=\frac{{{(120)}^{2}}}{2\times 0.12}\] \[\Rightarrow \] \[a=-60,000\,\,m/{{s}^{2}}\] Resistive force \[F=ma\] \[\Rightarrow \] \[F=0.003\times 60,000\] F = 1800 N