Q8 / 46 · NTA Abhyas (JEE Main) 2020 · Physics · Motion In One Dimension

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is 4 cm and that of the iron plate is 2 cm. A bullet fired goes through the wood first and then penetrates 1 cm into iron. A similar bullet fired with the same velocity from the opposite direction goes through iron first and then penetrates 2 cm into the wood. If a1 and a2 be the retardation offered to the bullet by wood and iron plates respectively, then

  • A
    a1=2a2
  • Correct answer
    B
    a2=2a1
  • C
    a1=a2
  • D
    Data insufficient

Solution

Let a1and a2be the retardations offered to be bullet by wood and iron respectively.

For A→B→C,

v12-u2=2a14, and 02-v12=2a2(1)

Adding, we get

-u2=2(4a1+a2) ...(i)

For A′→B′→C′,

v22-u2=2a22

and 02-v22=2a12

Adding, we get

-u2=2(2a1+2a2) ....(ii)

Equating Eqs. (i) and (ii) and solving, we get

4a1+a2=2a1+2a2

⇒ a2=2a1

Hence, the correct answer is option: 'B'.

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