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  • Help me understand! A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

  • Option 1)

    0, 1

  • Option 2)

    1, 1

  • Option 3)

    1, 0.5

  • Option 4)

    0, 2

 

Answers (1)

best_answer

As discussed in concept

Coffecient of Restitution (e) -

e= frac{v_{2}-v_{1}}{u_{2}-u_{1}}

- wherein

Ratio of relative velocity after collision to relative velocity before collision.

 

 v_{1} = 2ms^{-1}, v_{2}=0

m_{1} = m (say) \:\: m_{2}=2m

v_{1}^{1}=?\:\: v_{2}^{1}=?

e=\frac{v_{1}^{1}-v_{2}^{1}}{v_{2}-v_{1}} - (i)

From conservation of momentum

2m=mv_{1}^{1}+2mv_{2}^{1} - (ii)

From equation (i) 0.5= \frac{v_{2}^{1}-v_{1}^{1}}{2} = v_{2}^{1} = 1+v_{1}^{1}

From equation (ii)

2=v_{1}^{1}+2+2v_{1^{1}}\Rightarrow v_{1}^{1}=0 and v_{2}^{1} = 1 ms^{-2}


Option 1)

0, 1

This solution is correct

Option 2)

1, 1

This solution is incorrect

Option 3)

1, 0.5

This solution is incorrect

Option 4)

0, 2

This solution is incorrect

Posted by

prateek

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