Q. 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 2cm into wood. If $a_{1}$ and $a_{2}$be the retardation offered to the bullet by wood and iron plates respectively, then
A) $t_{1} + t_{2}$
B) $a_{2} = 2a_{1}$
C) $a_{1} = a_{2}$
D) Data insufficient
Explanation
(b) Let $a_{1}$and $a_{2}$be the retardations offered to be bullet by wood and iron respectively.
For $A \rightarrow B \rightarrow C,$
$v_{1}^{2} - u^{2} = 2a_{1}(4),$ and $0^{2} - v_{1}^{2} = 2a_{2}(1)$
Adding, we get
$- u^{2} = 2(4a_{1} + a_{2})$ ...(i)
For $A^{'} \rightarrow B^{'} \rightarrow C^{'},$
$v_{2}^{2} - u^{2} = 2a_{2}(2)$
and $0^{2} - v_{2}^{2} = 2a_{1}(2)$
Adding, we get
$- u^{2} = 2(2a_{1} + 2a_{2})$ ….(ii)
Equating Eqs. (i) and (ii) and solving, we get
$4a_{1} + a_{2} = 2a_{1} + 2a_{2}$
$\Rightarrow \ a_{2} = 2a_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.