Question

A mortar fires a shell of mass $M$ which explodes into two pieces of mass $\frac{M}{5}$ and $\frac{4M}{5}$ at the top of the trajectory. The smaller mass falls very close to the mortar. In the same time the bigger piece lands a distance $D$ from the mortar. The shell would have fallen at a distance $R$ from the mortar if there was no explosion. The value of $D$ is $($ Neglect air resistance $)$

• A. $\frac{3R}{2}$
• B. $\frac{4R}{3}$
• C. $\frac{5R}{4}$
• D. $none$ $of$ $these.$

Answer 1

Answer: (C)

$\frac{5R}{4}$

The CM will have the same trajectory as in the case without explosion.
Take the $x-$cordinate of the point of explosion as the origin.
Since the mortar would have fallen at a distance R from the point of explosion if there were no explosion, the co-ordinate of CM will be $R$.

$m_1=\frac{M}{5}$;

$m_2=\frac{4M}{5}$

$X_{CM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$;

$x_1=0$;
$x_2=R$;
Substituting $x_1$ and $x_2$;

$X_{CM}=R=\frac{\frac{M}{5}\times 0+\frac{4M}{5}\times D}{\frac{M}{5}+\frac{4M}{5}}$;

$\Rightarrow D=\frac{5}{4}R$