Two objects of masses 100 g and 200 g are moving along the same line and direction, with velocities $2 m s^{- 1}$ and $1 m s^{- 1}$ , respectively. They collide and after the collision, the second object moves with a velocity of $1.67 m s^{- 1}$ . Determine the velocity of the first object:

0.66 m s^{- 1}

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0.55 m s^{- 1}

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1.66 m s^{- 1}

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0.66 m s^{- 2}

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Solution

The correct option is A $0.66 m s^{- 1}$
Before Collision After collision
A B A B
100 g 200g $\to$ 100g 200g
2m/s 1m/s $v = ?$ $1.67 m s^{- 1}$
Let the 100 g and 200 g objects be A and B as shown in above figure.
Initial momentum of A $= \frac{100}{1000} \times 2 = 0.2 k g m s^{- 1}$
Initial momentum of B $= \frac{200}{1000} \times 1 = 0.2 k g m s^{- 1}$
$∴$ Total momentum of A and B before collision
$= 0.2 + 0.2 = 0.4 k g m s^{- 1}$
Let the velocity of A after collision $= v$
$∴$ Momentum of A after collision $= \frac{100}{1000} \times v = 0.1 v$
Also, momentum of B after collision
$= \frac{200}{1000} \times 1.67 = 0.334 k g m s^{- 1}$
$∴$ Total momentum of A and B after collision
$= 0.1 \times v + 0.334$
Using the law of conservation of momentum, momentum of A and B after collision $=$ momentum of A and B before collision
$0.1 \times v + 0.334 = 0.4$
$0.1 \times v = 0.4 - 0.334$
$\Rightarrow v = \frac{0.066}{0.1} = 0.66 m s^{- 1}$

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Two objects of masses 100 g and 200 g are moving along the same line and direction, with velocities 2ms−1 and 1ms−1, respectively. They collide and after the collision, the second object moves with a velocity of 1.67ms−1. Determine the velocity of the first object:

Two objects of masses 100 g and 200 g are moving along the same line and direction, with velocities $2 m s^{- 1}$ and $1 m s^{- 1}$ , respectively. They collide and after the collision, the second object moves with a velocity of $1.67 m s^{- 1}$ . Determine the velocity of the first object: