Physics-
General
Easy

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 2cm into wood. If a subscript 1 end subscript and a subscript 2 end subscriptbe the retardation offered to the bullet by wood and iron plates respectively, then

  1. t subscript 1 end subscript plus t subscript 2 end subscript  
  2. a subscript 2 end subscript equals 2 a subscript 1 end subscript  
  3. a subscript 1 end subscript equals a subscript 2 end subscript  
  4. Data insufficient  

The correct answer is: a subscript 2 end subscript equals 2 a subscript 1 end subscript


    Let a subscript 1 end subscriptand a subscript 2 end subscriptbe the retardations offered to be bullet by wood and iron respectively.
    For A rightwards arrow B rightwards arrow C comma
    v subscript 1 end subscript superscript 2 end superscript minus u to the power of 2 end exponent equals 2 a subscript 1 end subscript open parentheses 4 close parentheses comma and 0 to the power of 2 end exponent minus v subscript 1 end subscript superscript 2 end superscript equals 2 a subscript 2 end subscript left parenthesis 1 right parenthesis
    Adding, we get
    negative u to the power of 2 end exponent equals 2 left parenthesis 4 a subscript 1 end subscript plus a subscript 2 end subscript right parenthesis(i)
    For A to the power of ´ end exponent rightwards arrow B to the power of ´ end exponent rightwards arrow C to the power of ´ end exponent comma
    v subscript 2 end subscript superscript 2 end superscript minus u to the power of 2 end exponent equals 2 a subscript 2 end subscript open parentheses 2 close parentheses
    and 0 to the power of 2 end exponent minus v subscript 2 end subscript superscript 2 end superscript equals 2 a subscript 1 end subscript open parentheses 2 close parentheses
    Adding, we get
    negative u to the power of 2 end exponent equals 2 left parenthesis 2 a subscript 1 end subscript plus 2 a subscript 2 end subscript right parenthesis(ii)
    Equating Eqs. (i) and (ii) and solving, we get
    4 a subscript 1 end subscript plus a subscript 2 end subscript equals 2 a subscript 1 end subscript plus 2 a subscript 2 end subscript
    rightwards double arrow blank a subscript 2 end subscript equals 2 a subscript 1 end subscript

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