Centre of Mass 3 Question 24
27. A point mass of $1 kg$ collides elastically with a stationary point mass of $5 kg$. After their collision, the $1 kg$ mass reverses its direction and moves with a speed of $2 ms^{-1}$. Which of the following statement(s) is/are correct for the system of these two masses?
(2010)
(a) Total momentum of the system is $3 kg-ms^{-1}$
(b) Momentum of $5 kg$ mass after collision is $4 kg-ms^{-1}$
(c) Kinetic energy of the centre of mass is $0.75 J$
(d) Total kinetic energy of the system is $4 J$
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Answer:
Correct Answer: 27. (a, d)
Solution:
$$ \begin{aligned} -2 & =\frac{1-5}{1+5} v _1+0 \quad\left(\text { as } v _2=0\right) \\ \therefore \quad v _1 & =3 ms^{-1} \\ v _2^{\prime} & =\frac{m _2-m _1}{m _1+m _2} v _2+\frac{2 m _1}{m _1+m _2} v _1=1 ms^{-1} \\ P _{CM} & =P _i=(1)(3)=3 kg-m / s \\ P _5^{\prime} & =(5)(1)=5 kg-m / s \\ K _{CM} & =\frac{p _{CM}^{2}}{2 M _{CM}}=\frac{9}{2 \times 6}=0.75 J \\ K _{\text {total }} & =\frac{1}{2} \times 1 \times(3)^{2}=4.5 J \end{aligned} $$
