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

Step-by-step solution

Given, velocity of the bullet v=100 ~ms ⁻¹ Let, thickness of one plank, t=s According to third equation of motion, we get v²-u²=2 a s(0)-(100)²=2 a (2 s) ( two planks are penetrated) -1000=4 a s . (i) When velocity of bullet is doubled, v=200 ~ms ⁻¹ Applying third equation of motion again, we get 0-(200)²=2 a (n s) (where, n is number of planks) -40000=2 a n s From Eqs. (i) and (ii), we get -40000 -10000 = 2 a n s 4 a s n=8 Hence, 8 planks can be penetrated by the same bullet if speed is doubled.