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  4. A particle of mass 3 m is projected from the ground at some angle with horizontal. The horizontal range is R. At the highest point of its path it breaks into two pieces m and 2 m. The smaller mass comes to rest and larger mass finally falls at a distance x from the point of projection where x is equal to

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Q. A particle of mass $3\, m$ is projected from the ground at some angle with horizontal. The horizontal range is $R$. At the highest point of its path it breaks into two pieces $m$ and $2 m$. The smaller mass comes to rest and larger mass finally falls at a distance $x$ from the point of projection where $x$ is equal to

Laws of Motion

Solution:

$x _{ cm }=\frac{ m _{1} x _{1}+ m _{2} x _{2}}{ m _{1}+ m _{2}}$
$R =\frac{ m \left(\frac{ R }{2}\right)+2 m \left( x _{2}\right)}{3 m } $
$\Rightarrow x _{2}=\frac{5 R }{4}$
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