A shell of mass $10kg$ is moving with a velocity of $10m{s}^{-1}$ when it blasts and forms two parts of mass $9kg$ and $1kg$ respectively. If the first mass is stationary, the velocity of the second is

The correct option is C

$100m{s}^{-1}$

Step 1. Given data:

The initial mass of the shell $\left(m\right)$ $=10kg$

The velocity of the shell $\left(v\right)$ $=10m{s}^{-1}$

Mass of the first part of the shell $\left(m_1\right)$ $=9kg$

Mass of the second part of the shell $\left(m_2\right)$ $=1kg$

The velocity of the first part of the shell $\left(v_1\right)$ $=0m{s}^{-1}$ (as it is stationary)

assume the velocity of the second shell as $v_2$

Step 2. Finding the velocity of the second shell:

By the principle of conservation of momentum we have,

$mv=m_1{v}_1+m_2{v}_2$

Putting the values, we get

$\Rightarrow$ $\left(10\times 10\right)=\left(9\times 0\right)+\left(1\times v_2\right)$

$\Rightarrow$ $v_2=100m{s}^{-1}$

Hence, option (C) is correct.