Question

A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :

• A. 16 km
• B. 1 km
• C. 10 km
• D. 2 km

Answer 1

The Correct Option is C

The correct option is(C): 10 km

\(X _{ COM }=\frac{ m _{1} x _{1}+ m _{2} x _{2}}{ m _{1}+ m _{2}}\)
\(R =\frac{\frac{ M }{4} x +\frac{3 M }{4} \times \frac{ R }{2}}{ M }\)

Horizontal range is given as
\(r_{\frac{M}{4}}=\frac{r}{2}+d=2+8=10km\)
\(=10 Km\)