Question

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4\text{cm}$ and that of iron plate is $2cm$. A bullet fired goes through the wood first and then penetrates $1cm$ into the iron. A similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\text{cm}$ into the wood. If $a_1$ and $a_2$ be the retardation offered to the bullet by the 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 $a_2=2a_1$

Let $a_1$ and $a_2$ be the retardations offered to the bullet by wood and iron, respectively.

For $A\to B\to C$
$v_1^2-u^2=2a_1\left(4\right)$ and
$0^2-v_1^2=2a_2\left(1\right)$
Adding we get
$-u^2=(4a_1+a_2)2\dots \dots \left(1\right)$

For $A^{{}^{\prime }}\to B^{{}^{\prime }}\to C^{{}^{\prime }}$
$v_2^2-u^2=2a_2\left(2\right)$ and
$0-v_2^2=2a_1\left(2\right)$
Adding we get
$-u^2=(2a_1+2a_2)2\dots \dots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$a_2=2a_1$