An object flying in air with velocity (20i^ + 25j^ – 12k^) suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity (100i^+ 35j^+ 8k^). The velocity of the larger piece will be

# An object flying in air with velocity  suddenly breaks in two pieces whose masses are in the ratio 1: 5. The smaller mass flies off with a velocity . The velocity of the larger piece will be

1. A

2. B

3. C

4. D

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### Solution:

Let m be the mass of an object flying with velocity v in air. When it gets split into two pieces of masses in ratio 1 : 5, the mass of smaller piece is m/6 and of bigger piece is $\frac{5\mathrm{m}}{6}.$

This situation can be interpreted diagrammatically as below.

As, the object breaks in two pieces, so the momentum of the system will remains conserved, i.e. the total momentum (before breaking) = total momentum (after breaking)

$m\mathbf{v}=\frac{m}{6}{\mathbf{v}}_{1}+\frac{5m}{6}{\mathbf{v}}_{2}⇒\mathbf{v}=\frac{{\mathbf{v}}_{1}}{6}+\frac{5{\mathbf{v}}_{2}}{6}$

Given,

and

Putting these values in Eq. (i), we get

$\left(20\stackrel{^}{\mathbf{i}}+25\stackrel{^}{\mathbf{j}}-12\stackrel{^}{\mathbf{k}}\right)=\frac{\left(100\stackrel{^}{\mathbf{i}}+35\stackrel{^}{\mathbf{j}}+8\stackrel{^}{\mathbf{k}}\right)}{6}+\frac{5{\mathbf{v}}_{2}}{6}$

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