A) 6
B) 9
C) 11
D) 13
Correct Answer: B
Solution :
The final velocity after it passes the plank is \[\frac{19u}{20}.\] Let \[x\] be the thickness of the plank, the deceleration due to resistance of plank, is given by \[{{v}^{2}}={{u}^{2}}+2as\]where v is final velocity, u is initial velocity, a is acceleration and s is displacement. Here \[v=\frac{19}{20}u\] \[\therefore \] \[{{\left( \frac{19}{20}u \right)}^{2}}={{u}^{2}}+2\,ax\] \[\Rightarrow \] \[2\,ax=\frac{-39}{400}{{u}^{2}}\] Suppose the bullet is stopped after passing through n such planks. Then the distance covered by bullet is \[nx\]. \[\therefore \] \[0={{\left( \frac{19}{20} \right)}^{2}}{{u}^{2}}+2\,anx\] \[\Rightarrow \] \[-{{\left( \frac{19}{20} \right)}^{2}}{{u}^{2}}=n\times \frac{-39}{400}{{u}^{2}}\] \[\Rightarrow \] \[n=\frac{361}{39}\approx 9\]You need to login to perform this action.
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