Question

A shell fired from ground get 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 the ground

• 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 pieces will be $m$ and distance between them is $x$.
According to question


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