Question

An object at rest is suddenly broken apart into two fragments by an explosion. The first fragment (with mass m1) acquires twice the kinetic energy of the second one (with mass m2).
What is the ratio of their masses?

Answer 1

Answer:

m1 ÷ m2 = 1 ÷ 2

Explanation:

The ratio of their masses is as follows:

As it is given that the mass m1 is twice of mass m2

So the equation could be written as

$\frac{1}{2} m1 v1 v1 = 2 \times \frac{1}{2} m2 v2 v2\\\\\frac{m1}{m2} = \frac{2 v2 v2}{v1 v1} ..........(1)$

Here we used the  conservation of momentum

Prior to the explosion, the object is in rest so the momentum would be zero but after the explosion the total momentum would be  m1v1 + m2v2,  that is also zero.

So,

$m1 v1 + m2 v2 = 0\\\\m1 v1 = - m2 v2\\\\\frac{m1}{m2} = \frac{- v2}{v1}$

Now squaring to the both sides

m1 m1 ÷ (m2 m2) = v2 v2 ÷ (v1 v1) ........(2 )

Solved both the equations

After solving it, the ratio is

m1 ÷ m2 = 1 ÷ 2