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 from opposite direction goes through iron first and then penetrates 2 cm into wood. If a₁ and a₂ be the retardations offered to the bullet by wood and iron plates respectively then.

(a) a₁ = 2a₂

(b) a₂= 2a₁

(c) a₁ = a₂

(d) Data insufficient

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Solution

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$L e t t h e v e l o c i t y w i t h w h i c h b u l l e t e n t e r s t h e w o o d e n n p l a n k b e u a n d v e l o c i t y a t t h e i n t e r f a c e o f i r o n a n d w o o d e n p l a n k b e v . c o n s i d e r i n g m o t i o n i n t h e w o o d e n p l a n k v^{2} - u^{2} = - 2 a \times (4) v^{2} = u^{2} - 8 a_{1} c o n s i d e r i n g m o t i o n i n t h e i r o n p l a n k 0^{2} - v^{2} = - 2 a_{2} \times (1) 0 = v^{2} - 2 a_{2} 0 = u^{2} - 8 a_{1} - 2 a_{2} u^{2} = 8 a_{1} + 2 a_{2} . . . A c o n s i d e r i n g m o t i o n i n t h e i r o n p l a n k f i r s t {v_{1}}^{2} - u^{2} = - 2 a_{2} \times (2) {v_{1}}^{2} = u^{2} - 4 a_{2} c o n s i d e r i n g m o t i o n i n t h e w o o d e n p l a n k 0^{2} - {v_{1}}^{2} = - 2 a_{1} \times (2) {v_{1}}^{2} = 4 a_{1} u^{2} - 4 a_{2} = 4 a_{1} u^{2} = 4 a_{2} + 4 a_{1} . . . B f r o m e q n A a n d B 8 a_{1} + 2 a_{2} = 4 a_{2} + 4 a_{1} 4 a_{1} = 2 a_{2} a_{2} = 2 a_{1} R e g a r d s$

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Similar questions

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 plates is

2 cm

. A bullet fired goes through the wood first and then penetrates

1 cm

into the iron. A similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates

2 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 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