# A mass M breaks into two pieces in the ratio 1 : 3 while at rest. If the heavier has a speed of v, the speed of the lighter is

Dear Student,
Given,
A mass M breaks into two pieces in the ratio 1 : 3
Let the common mass fraction be x, then
one part will have mass x while the other will have mass 3x, such that
x+3x = M
So, x = M/4
Initially, the mass is at rest, i.e., initial momentum of the mass is 0.
After breaking, the heavier mass 3x = 3M/4 moves with a velocity v.
Let u be the velocity with which the smaller mass x = M/4 moves be u.
Then, from conservation of linear momentum, we get
$xu+3xv=0\phantom{\rule{0ex}{0ex}}\frac{Mu}{4}=-\frac{3Mv}{4}\phantom{\rule{0ex}{0ex}}u=-3v$
So, the speed of the lighter mass is 3 times the speed of the heavier mass and the lighter mass moves in a direction opposite to that of the heavier mass.

Regards

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