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Question

A body of mass 5 kg is moving along the x-axis with a velocity 2ms1. Another body of mass 10 kg is moving along the y-axis with a velocity 3ms1. They collide at the origin and stick together. The final velocity of the combined mass is

A
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C
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Solution

The correct option is C
Momentum of 5 kg mass (p1)=5×2=10kg ms1 along the x-axis. Momentum of 10 kg mass (p2)=103 kg ms1 along the y-axis. These two momenta are perpendicular to each other.
Therefore, the resultant initial momentum is
P=p21+p22=(10)2+(103)2=20 kg ms1
If v ms1 is the velocity of the combined mass, then the final momentum = (10 + 5) v = 15 v kg ms1
Now, from the principle of conservation of momentum, we have 15 v = 20 or v=43 ms1, which is choice (c).

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