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

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 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 (B) a2=2a1 (C) a1=a2 (D) Data insufficient

Tardigrade Admin · Accepted Answer

Let a1 and a2 be the retardations offered to be bullet by wood and iron respectively. For A arrow B arrow C, v12-u2=2a1(4), and 02-v12=2a2(.1.) Adding, we get -u2=2(.4a1+a2.) ...(i) For A'arrow B' arrow C' v22-u2=2a2(2) and 02-v22=2a1(2) Adding, we get -u2=2(.2a1+2a2.) ....(ii) Equating Eqs. (i) and (ii) and solving, we get 4a1+a2=2a1+2a2 ⇒ a2=2a1

$a_{1} = 2 a_{2}$

$a_{2} = 2 a_{1}$

$a_{1} = a_{2}$

Data insufficient

a1​=2a2​

a2​=2a1​

a1​=a2​

Data insufficient

$a_{1} = 2 a_{2}$

$a_{2} = 2 a_{1}$

$a_{1} = a_{2}$