Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u, and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be :

  • Option 1)

    \frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})

  • Option 2)

    \frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})

  • Option 3)

    \frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})

  • Option 4)

    \frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})

 

Answers (1)

As we learnt in 

Law of Consevation of Momentum -

 \vec{F}=\frac{\vec{dp}}{dt}

\vec{F}=0            then \vec{p}=constant

\vec{p}=\vec{p}_{1}+\vec{p}_{2}+\cdots =const

- wherein

\ast Independent of frame of reference

 

 

Pi = Py

m3u\hat{i}+3m[-ucos60\hat{i}+usin60\hat{j}]+2m[-2ucos60\hat{i}-2usin60\hat{j}]

=3mu\hat{i}+3m[\frac{-v}{2}\hat{i}+\frac{0\sqrt{3}\hat{j}}{2}]\Rightarrow \frac{u}{12}(\hat{-i}-\sqrt{3}\hat{j})


Option 1)

\frac{u}{12}(\hat{i}+\sqrt{3}\hat{j})

Incorrect

Option 2)

\frac{u}{12}(\hat{i}-\sqrt{3}\hat{j})

Incorrect

Option 3)

\frac{u}{12}(-\hat{i}+\sqrt{3}\hat{j})

Incorrect

Option 4)

\frac{u}{12}(-\hat{i}-\sqrt{3}\hat{j})

Correct

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