question_answer

A bullet moving with a speed of 100 \[m{{s}^{-1}}\]can just penetrate two planks of equal thickness. Then the number of such planks penetrated by the same bullet when the speed is doubled will be                                              [KCET 2004]

A)                 4

B)                    8

C)                 6             

D)                 10

Correct Answer: B

Solution :

             Let the thickness of each plank is s. If the initial speed of bullet is 100 m/s then it stops by covering a distance 2s By applying \[{{v}^{2}}={{u}^{2}}-2as\]Þ \[0={{u}^{2}}-2as\] \[s=\frac{{{u}^{2}}}{2a}\] \[s\propto {{u}^{2}}\] [If retardation is constant] If the speed of the bullet is double then bullet will cover four times distance before coming to rest i.e. \[{{s}_{2}}=4({{s}_{1}})=4(2s)\] Þ \[{{s}_{2}}=8s\] So number of planks required = 8