# A particle of mass M which is at rest splits up into two…

**Quick Navigation Panel**hide

**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:**

**Option A is incorrect.****Option B is correct. momentum before split = total momentum after split.****C is incorrect.****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.**

**You can freely add your own answers below or click the golden ASK A QUESTION BOTTON down this page to raise new related questions… OUR COMMUNITY OF EXPERTS WILL BE HAPPY TO TACKLE IT…**

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