The velocity of the bullet reduces by 1/20th of its initial velocity after passing through a plank. The maximum number of planks it can cross is N. Find (N − 5)
Physics · Mixed Chapter
JEE Mains

Question

The velocity of the bullet reduces by 1/20th of its initial velocity after passing through a plank. The maximum number of planks it can cross is N. Find (N − 5)

G1 Physics · Accepted Answer

Step 1: Let initial speed be u. After the first uniform plank the speed drops by u/20, to (19/20)u. Step 2: Energy lost in a plank (identical work against resistance) is ΔK=½m[u²−(19u/20)²]=½mu²(39/400). Step 3: Total initial kinetic energy is ½mu², enough for at most floor(400/39)=10 complete identical planks. The eleventh would stop the bullet. Step 4: N=10, hence N−5=5. Answer: 5.