A bullet moving with a speed of `100 ms^(-1)` can just penetrate into two planks of equal thickness. Then the number of such planks, if speed is doubled will be .

Options

A. 4
B. 6
C. 8
D. 10

Answer

C

Explanation

Given initial velocity of bullet in first case `(u_1)=100m//s` Initial number of planks `(n_1)=2`
Initial stopping distance `(s_1) =n_(1) x = 2x` ( where x is the thickness of one plank).
Initial velocity of bullet in seconds case `(u_2) = 200m//s` . Relation for the stopping distance (s) is `v^(2) =u^(2) +2as`
Since the bullet is just able to penetrate the planks , therefore its final velocity v = 0
Thus , `2as = -u^(2) " or " s prop u^(2) :. s_1/s_2 =((u_1)/u_2)=1/4`
Thus final number of planks `(n_2) = s_2/x = (8x)/x = 8`