A) 6
B) 10
C) 4
D) 8
Correct Answer: D
Solution :
Let the thickness of each plank is d. From. equation of motion \[{{\upsilon }^{2}}={{u}^{2}}+2\,as\] ... (i) Ist case; \[s=2\,d,\,u=100\,\,m{{s}^{-1}},\upsilon =0\] \[\therefore \] \[0={{(100)}^{2}}+2a\times 2d\] \[\Rightarrow \] \[4ad=-100\times 100\] \[\Rightarrow \] \[a=-\frac{100\times 100}{4d}\] \[\therefore \] \[a=-\frac{2500}{d}\] ... (2) (- ve sign stands for retardation) IInd case; Let the bullet with double the previous speed will penetrate n planks of equal thickness d. Now, \[\upsilon =0,\,u=200\,m{{s}^{-1}},a=-\frac{2500}{d},\,s=nd\] Using equation (1) again, we have \[0={{(200)}^{2}}-2\times \frac{2500}{d}\times nd\] \[\Rightarrow \] \[n=\frac{200\times 200}{2\times 2500}=8\]
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