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Question

# A body of mass 5 kg is moving along the x-axis with a velocity 2ms−1. Another body of mass 10 kg is moving along the y-axis with a velocity √3ms−1. If they collide at the origin and stick together, then the final velocity of the combined mass is

A
3ms1
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B
(3+1)ms1
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C
43ms1
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D
None
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Solution

## The correct option is C 43ms−1Momentum of 5 kg mass (p1)=5×2=10kg ms−1 along the x-axis. Momentum of 10 kg mass (p2)=10√3 kg ms−1 along the y-axis. These two momenta are perpendicular to each other. Therefore, the resultant initial momentum is P=√p21+p22=√(10)2+(10√3)2=20 kg ms−1 If v ms−1 is the velocity of the combined mass, then the final momentum = (10 + 5) v = 15 v kg ms−1 Now, from the principle of conservation of momentum, we have 15 v = 20 or v=43 ms−1, which is choice (c).

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