A body of mass 2 \; kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed.What is the mass of the second body ?

  • Option 1)

    1.0 \: kg

  • Option 2)

    1.5\: kg

  • Option 3)

     1.8\: kg

  • Option 4)

    1.2 \: kg

 

Answers (1)

m\Rightarrow mass of A body = 2kg

u\Rightarrow initial velocity of A body 

M\Rightarrow mass of B body

A                      B

m\rightarrow u        M\Rightarrow               m\rightarrow \frac{u}{4}           M\rightarrow V

                       rest 

 

V-\frac{u}{4}=u   (from e=1)

\Rightarrow V=\frac{5u}{4}

momentum balance

mu=\frac{mu}{4}+MV

\Rightarrow \frac{3mu}{4}=M\left ( \frac{5u}{4} \right )

\Rightarrow M=\frac{3m}{5}

            =\frac{3\times 2}{5}

     M=\frac{6}{5}kg

         =1.2\; kg


Option 1)

1.0 \: kg

Option 2)

1.5\: kg

Option 3)

 1.8\: kg

Option 4)

1.2 \: kg

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