question_answer

A rifle bullet loses 1/20th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is              [EAMCET  1987; AFMC 2004]

A)                 5             

B)                 10

C)                 11          

D)                 20

Correct Answer: C

Solution :

                    Let the thickness of one plank is s if bullet enters with velocity u then it leaves with velocity \[v=\left( u-\frac{u}{20} \right)=\frac{19}{20}u\]                 from \[{{v}^{2}}={{u}^{2}}-2as\] Þ \[{{\left( \frac{19}{20}u \right)}^{2}}={{u}^{2}}-2as\]Þ \[\frac{400}{39}=\frac{{{u}^{2}}}{2as}\]                 Now if the n planks are arranged just to stop the bullet then again from \[{{v}^{2}}={{u}^{2}}-2as\]                 \[0={{u}^{2}}-2ans\]                 Þ \[n=\frac{{{u}^{2}}}{2as}=\frac{400}{39}\]                 Þ \[n=10.25\]                 As the planks are more than 10 so we can consider  n = 11