A body of mass m1 moving with uniform velocity of 40 m/s collides with another mass m2 at rest and then the two bodies begins to move together with a uniform velocity of 30 m/s. The ratio of their masses (m1/m2) is :-34
Question
A body of mass m1 moving with uniform velocity of 40 m/s collides with another mass m2 at rest and then the two bodies begins to move together with a uniform velocity of 30 m/s. The ratio of their masses (m1/m2) is :-34
Solution
The problem is based on the principle of conservation of momentum. According to this principle, the total momentum of an isolated system of particles is constant, provided no external force acts on it.
The initial momentum of the system is the momentum of the moving body, which is the product of its mass m1 and its velocity 40 m/s. So, initial momentum = m1 * 40.
The final momentum of the system is the combined momentum of the two bodies moving together. This is the product of the total mass (m1 + m2) and their common velocity 30 m/s. So, final momentum = (m1 + m2) * 30.
According to the conservation of momentum, initial momentum = final momentum.
So, m1 * 40 = (m1 + m2) * 30.
Solving this equation for m1/m2 gives the ratio of the masses.
40m1 = 30m1 + 30m2
10m1 = 30m2
m1/m2 = 30/10 = 3
So, the ratio of their masses m1/m2 is 3. But in the question, it is given that the ratio is 34, which seems to be a mistake.
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