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

Question

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]

Smart Achievers · Accepted Answer

(1, 3)

According to law of conservation of linear momentum

$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$

$1 \times u_{1} + 5 \times 0 = 1 (- 2) + 5 (v_{2})$

$\Rightarrow u_{1} = - 2 + 5 v_{2}$ ...(i)

The coefficient of restitution

$e = \frac{v_{2} - v_{1}}{u_{1} - u_{2}} = 1$

$\Rightarrow 1 = \frac{v_{2} - (- 2)}{u_{1} - 0} \Rightarrow u_{1} = v_{2} + 2$ ...(ii)

$From eq (i) & (ii), u_{1} = 3 m/s and v_{2} = 1 m/s$

Hence total momentum of the system = 3 kg m/s and ${K.E}_{cm} = 0.75 J$

Solution

Q.
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]

1 Total momentum of the system is $3 {kg ms}^{- 1}$

2 Momentum of 5 kg mass after collision is $4 {kg ms}^{- 1}$

3 Kinetic energy of the centre of mass is 0.75 J

4 Total kinetic energy of the system is 4J

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