Question

A $30kg$ sphere, moving with a velocity $48m/s$, splits into parts after explosion. The masses of these fragments are $18kg$ and $12kg$. If the heavier fragment comes to rest after explosion, the velocity of second fragment will be :

• A. $80m/s$
• B. $100m/s$
• C. $110m/s$
• D. $120m/s$

Answer 1

The correct option is D $120m/s$

Let, the mass of sphere before collision is $M=30Kg$ and its velocity is $V=48m{s}^{-1}$.
After collision it splits into masses $m_1=18Kg$ and $m_2=12Kg$. The velocity of heavier mass s zero i.e. $v_1=0$ and lighter mass is $v_2$
Now according to the law of conservation of momentum we get
$MV=m_1{v}_1+m_2{v}_2$

$\left(30\right)\left(48\right)=\left(18\right)\left(0\right)+\left(12\right)\left(v_2\right)$

$V_2=\frac{\left(30\right)\left(48\right)}{12}$

$V_2=\left(30\right)\left(4\right)=120m{s}^{-1}$