Question

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 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 opposite direction goes through iron first and then penetrates 2 cm into wood. If $a_1$ and $a_2$ be the retardations offered to the bullet by wood and iron plates respectively then

• A. $a_1=2a_2$
• B. $a_2=2a_1$
• C. $a_1=a_2$
• D. data insufficient

Answer 1

The correct option is B

$a_2=2a_1$

Case-1: $0^2-u^2=2(-a_1)\left(4\right)+2(–a_2)\left(1\right)\dots \left(i\right)$

Case-2: $0^2-u^2=2(-a_2)\left(2\right)+2(-a_1)\left(2\right)\dots \left(ii\right)$

From (i) and (ii)

$a_2=2a_1$