Question

An explosion blows a stationary rock into three parts. Two parts of masses $1kg$ and $2kg$ moves at right angles to one another with velocities $12m{s}^{-1}$ and $8m{s}^{-1}$, respectively. If the velocity of third part is $4m{s}^{-1}$, the mass of the rock is

• A. 8 kg
• B. 5 kg
• C. 17 kg
• D. 3 kg

Answer 1

Answer: (A)

Given, $m_1=1kg,m_2=2kg$,
$v_1=12m{s}^{-1},v_2=8m{s}^{-1}$ and $v_3=4m{s}^{-1}$
Since, in the explosion of stationary rock, the momentum is conserved,
so $p_i=p_f$
$0=p_f=p_1+p_2+p_3$
where, $p_1=m_1{v}_1,p_2=m_2{v}_2$ and $p_3=m_3{v}_3$
$p_3=-\left(p_1+p_2\right)$
$p_3=\sqrt{p_1^2+p_2^2+2p_1\cdot p_2\cos \theta }$
$p_3=\sqrt{12^2+16^2+2\times 12\times 16\cos 90^{\circ }}$
$P_3=20$
$m_3{v}_3=m_3\times 4=20$
$\Rightarrow m_3=5kg$
Hence, the mass of the rock is,
$m=m_1+m_2+m_3$
$m=1+2+5=8kg$