Question

An explosion blows a rock into three pieces. Two pieces go off at right angles to each other. One piece of these two has mass $1kg$ and moves with velocity $12m/s$ ; other has mass $2kg$ and moves with velocity $8m/s$. If the velocity of the third piece is $40$ m/sec, then its mass is.

• A. $5kg$
• B. $0.5kg$
• C. $0.25kg$
• D. $0.75kg$

Answer 1

Answer: (B)

$0.5kg$

Use law of conservation of momentum.

Initial Momentum $=$ Final Momentum

$M\overrightarrow{U}=m_1\overrightarrow{v_1}+m_2\overrightarrow{v_2}+m_3\overrightarrow{v_3}$

Here, $U=0$, $m_1=1$ kg, $m_2=12$ kg, $v_1=12\hat{i}$, $v_2=8\hat{j}$

$\Rightarrow 0=1\times 12\hat{i}+2\times 8\hat{j}+m_3\overrightarrow{v_3}$

$\Rightarrow m_3\overrightarrow{v_3}=-12\hat{i}-16\hat{j}\Rightarrow |m_3\overrightarrow{v_3}|=20$

$\Rightarrow m\times 40=20\Rightarrow m=0.5kg$