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Question: A particle of mass 1g having velocity \(3\widehat{i} - 2\widehat{j}\) has a glued impact with anothe...

A particle of mass 1g having velocity 3i^−2j^3\widehat{i} - 2\widehat{j} has a glued impact with another particle of mass 2g and velocity as 4j^−6k^4\widehat{j} - 6\widehat{k}. Velocity of the formed particle is

A

5.6ms−15.6ms^{- 1}

B

0

C

6.4ms−16.4ms^{- 1}

D

4.6ms−14.6ms^{- 1}

Answer

4.6ms−14.6ms^{- 1}

Explanation

Solution

By conservation of momentum

mu→1+m2u→2=(m1+m2)V→m{\overrightarrow{u}}_{1} + m_{2}{\overrightarrow{u}}_{2} = (m_{1} + m_{2})\overrightarrow{V}

∴ V→=m1u→1+m2u→2m1+m2\overrightarrow{V} = \frac{m_{1}{\overrightarrow{u}}_{1} + m_{2}{\overrightarrow{u}}_{2}}{m_{1} + m_{2}} =1(3i−2j^)+2(4j−6k^)m1+m2= \frac{1(3i - 2\widehat{j}) + 2(4j - 6\widehat{k})}{m_{1} + m_{2}}

=3i+6j−12k^(1+2)=i^+2j^−4k^= \frac{3i + 6j - 12\widehat{k}}{(1 + 2)} = \widehat{i} + 2\widehat{j} - 4\widehat{k}

∣V→∣=(1)2+(2)2+(−4)2=1+4+16=4.6m⥂s−1|\overrightarrow{V}| = \sqrt{(1)^{2} + (2)^{2} + ( - 4)^{2}} = \sqrt{1 + 4 + 16} = 4.6m ⥂ s^{- 1}.