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5.Work, Energy, Power and Collision
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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
$4$
B
$8$
C
$6$
D
$10$
Solution
(b)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$
Standard 11
Physics
