Question contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.

Option 1)

Statement-1 is true, Statement-2 is false.

Option 2)

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

Option 4)

Statement-1 is false, Statement-2 is true.

Answers (1)

As we learnt in

Perfectly Inelastic Collision -

v= \frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}

- wherein

Two bodies stick together after the collision ,so there will be a final common velocity (v)

m_{1},m_{2}= masses

v_{1}=\: initial \: velocity \: mass\: m_{1}

v_{2}=\: initial \: velocity \: mass\: m_{2}

 

 From conservation of momentum 

m{v}_{i}=(m+M)V_{f}

0.50\times 2=(1.5)V_{f}

V_{f}=\frac{2}{3}\ m/s

Initial Kinetic energy K_{i}=\frac{1}{2}mv_{i}^{2}=\frac{1}{2}\times0.5\times2^{2}=1J

Final Kinetic energy =\frac{1}{2}v_{f}^{2}(m+M)=\frac{1}{2}\times0.5\times\left(\frac{2}{3} \right )^{2}=\frac{1}{2}\times\left(1.5 \right )\times\frac{4}{9}=\frac{1}{3} J

Loss of energy = initial kinetic energy + Final Kinetic energy

=1J-\frac{1}{3}J=0.67J


Option 1)

Statement-1 is true, Statement-2 is false.

This is an incorrect option.

Option 2)

Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

This is the correct option.

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

This is an incorrect option.

Option 4)

Statement-1 is false, Statement-2 is true.

This is an incorrect option.

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