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Two identical balls A and B having velocities of 0.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}} and - 0.3{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}} respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be

  • Option 1)

    \begin{array}{*{20}c} { - 0.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .3}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

  • Option 2)

    \begin{array}{*{20}c} {0.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & { - {\rm 0}{\rm .3}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

  • Option 3)

    - \begin{array}{*{20}c} {0.3{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .5}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

  • Option 4)

    \begin{array}{*{20}c} {0.3{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .5}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

 

Answers (1)

 

Perfectly Elastic Collision -

Law of conservation of momentum and that of Kinetic Energy hold good.

- wherein

frac{1}{2}m_{1}u_{1}^{2}+frac{1}{2}m_{2}u_{2}^{2}= frac{1}{2}m_{1}v_{1}^{2}+frac{1}{2}m_{2}v_{2}^{2}

m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}

m_{1},m_{2}:masses

u_{1},v_{1}:initial : and: final : velocity: of : the: mass m_{1}

u_{2},v_{2}:initial : and: final : velocity: of : the: mass m_{2}

 

 When the identical balls collide head on thier velocities are exchanged.


Option 1)

\begin{array}{*{20}c} { - 0.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .3}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

Incorrect option

Option 2)

\begin{array}{*{20}c} {0.5{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & { - {\rm 0}{\rm .3}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

Correct option

Option 3)

- \begin{array}{*{20}c} {0.3{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .5}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

Incorrect option

Option 4)

\begin{array}{*{20}c} {0.3{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} & {{\rm and}} & {{\rm 0}{\rm .5}{{\rm m} \mathord{\left/ {\vphantom {{\rm m} {\rm s}}} \right. \kern-\nulldelimiterspace} {\rm s}}} \\ \end{array}

Incorrect option

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Vakul

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