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A particle of mass M which is at rest splits up into two. if the mass and the velocity of one of the particles are m and v respectively, calculate the velocity of the second particle.

QUICK ANSWER…

B

DETAILS…

Momentum before split = total momentum after split

Momentum = mass X velocity

If the mass of the particle is M,

Momentum before split = M X 0 = 0 (because the particle is at rest)

Mass of one of the split particles = m, and its velocity is given as v. therefore, its momentum will be = mv

Mass of the second particle = M – m, and let the velocity of the second particle be V.

Since momentum before split = total momentum after split,

0 = momentum of particle 1 + momentum of particle 2

0 = mv + (M – m)V

mv + (M – m)V = 0

mv = –(M – m)V

or mv = (m – M)V

therefore, mv/(m – M) = V

so, V = mv/(m – M)

Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is correct. momentum before split = total momentum after split.
3. C is incorrect.
4. D is not the correct answer. First of all, momentum is a vector, and so, simply solving with (M – m)V = mv, to arrive at V = mv/(M – m), ignores this direction and results in a wrong answer.

KEY-POINTS…

You may please note these/this:

• Velocity of the mass before split is zero because the body is at rest.
• Please note that momentum is a scalar quantity and the direction of its velocity is crucial.

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/ culled from 2016 JAMB-UTME physics past question 29 /