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

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 2sBy applying v2=u2−2as⇒0=u2−2ass=u22a   s∝u2   [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.  s2=4(s1)=4(2s)⇒s2=8sSo number of planks required = 8