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 \[(0.12\,m=s)\] inside the block. Since, it comes to rest the final velocity \[(v)\] is zero. From equation of motion, we have \[{{v}^{2}}={{u}^{2}}+2as\] Here,  \[v=0,u=120\,m/s,\,s=0.12\,m\]                 \[\Rightarrow \]               \[a=-\frac{{{u}^{2}}}{2s}=\frac{{{(120)}^{2}}}{2\times 0.12}\]                 \[\Rightarrow \]               \[a=-60,000\,m/{{s}^{2}}\]                 Resistive force \[F=ma\]                 \[\Rightarrow \]               \[F=0.03\times 60,000\]                 \[F=1800\,N\]