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
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
$4$
$8$
$6$
$10$
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
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 ${v^2} = {u^2} - 2as$
$⇒$ $0 = {u^2} - 2as$ $s = \frac{{{u^2}}}{{2a}}$
$s \propto {u^2}$ [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. ${s_2} = 4({s_1}) = 4(2s)$
$⇒$ ${s_2} = 8s$
So number of planks required $ = 8$
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