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Q.

Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2m/s and 1m/s respectively. They collide and after the collision the first object moves at a velocity of 1.67m/s the velocity of the second object is

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a

$5.08 m / s$

b

$2.54 m / s$

c

$11.60 m / s$

d

$1.16 m / s$

answer is B.

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Detailed Solution

$\begin{array}{l} m_{1} = 100 g, m_{2} = 200 g \\ u_{1} = 2 m / s, u_{2} = 1 m / s, v_{1} = 1 .67 m / s, v_{2} = ? \\ m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} \\ m_{1} u_{1} + m_{2} u_{2} - m_{1} v_{1} = m_{2} v_{2} \\ m_{1} (\frac{u_{1} - v_{1}}{m_{2}}) + u_{2} = v_{2} \\ 100 (\frac{2 - 1 .67}{200}) + 1 = v_{2} \\ \frac{2 - 1 .67}{2} + 1 = v_{2} \\ \frac{0 .33}{2} + 1 = v_{2} \\ = 1 .16 m / s \end{array}$

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