Question

A shell fired from the ground explodes at the highest point in its path into two pieces of equal masses. One of the pieces retraces its path. Distance between the two pieces when both lands on the ground is :

• A. $\frac{u^2\sin 2\theta }{g}$
• B. $\frac{u^2\sin 2\theta }{2g}$
• C. $\frac{2u^2\sin 2\theta }{g}$
• D. $\frac{u^2\sin 2\theta }{4g}$

Answer 1

The correct option is C $\frac{2u^2\sin 2\theta }{g}$

Let us suppose, mass of the shell is $2m$, then mass of each piece will be $m$ and distance between them is $x$.
According to question


We know that in explosion, internal forces operates and $\sum F_{internal}=0$. Therefore, path of centre of mass will not get effected and it will land on the ground at the distance $R$$($Range$)$.
Now, $R=\frac{u^2\sin 2\theta }{g}$ ............(1)
Also, $R=\frac{m\times 0+m\times x}{2m}$
$[r_{c.o.m}=\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}]$
$[\text{Here},r_1=0,r_2=x]$
$\Rightarrow x=2R$
$\Rightarrow x=\frac{2u^2\sin 2\theta }{g}$ $[$ from (1) $]$
Distance between two pieces when both lands on the ground is $\frac{2u^2\sin 2\theta }{g}$