Question

Three particles with masses $10,20$ and $40$ g are moving with velocities $10\hat{i},10\hat{j}$ and $10\hat{k}m/sec$ respectively. If due to some interaction the first particle comes to rest and the velocity of second becomes ($3\hat{i}+4\hat{j}m/sec$). Then the velocity of third particle after their interaction is:

• A. $\hat{i}+\hat{j}+5\hat{k}$
• B. $\hat{j}+10\hat{k}$
• C. $\hat{i}+\hat{j}+10\hat{k}$
• D. $\hat{i}+3\hat{j}+10\hat{k}$

Answer 1

The correct option is D $\hat{i}+3\hat{j}+10\hat{k}$

Applying conservation of linear momentum,
$10\times 10\hat{i}+20\times 10\hat{j}+40\times 10\hat{k}=10\times 0+20\times (3\hat{i}+4\hat{j})+40\overrightarrow{V}$
$\Rightarrow \overrightarrow{V}=\hat{i}+3\hat{j}+10\hat{k}$