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Work

Question

A bullet moving with a speed of 100 ms^-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

Moderate

A

4
B

8
C

6
D

10

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 $v^{2} = u^{2} - 2 as \Rightarrow 0 = u^{2} - 2 as$
$s = \frac{u^{2}}{2 a} s \propto u^{2}$ [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. $s_{2} = 4 (s_{1}) = 4 (2 s) \Rightarrow s_{2} = 8 s$
So number of planks required = 8

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