# A 3.0 kg object is moving to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 6.0 kg object moving to the left at 2.0 m/s. What is the total kinetic energy after the collision? Option 1) 62 J Option 2) 25 J Option 3) 12 J Option 4) 0.0 J

As we discussed in concept

Perfectly Inelastic Collision -

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

- wherein

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

$\fn_jvn m_{1},m_{2}= masses$

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

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

$m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})V$

$V=\frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}=\frac{12+12}{9}=\frac{24}{9}=\frac{8}{3}\:ms^{-1}$

$K=\frac{1}{2}(m_{1}+m_{2})V^{2}=\frac{1}{2}.\:9\times (\frac{8}{3})^{2}$

$K=\frac{1}{2}.\:9\times \frac{64}{9}\:=\:32J$

Option 1)

62 J

This option is incorrect.

Option 2)

25 J

This option is incorrect.

Option 3)

12 J

This option is incorrect.

Option 4)

0.0 J

This option is incorrect.

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