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Question

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

A

3 ms1

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B

(3+1) ms1

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C

43 ms1

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D

34 ms1

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Solution

## The correct option is C 43 ms−1 Momentum of 5 kg mass, P1=5×2=10 kgms−1 along the x-axis Momentum of 10 kg mass, P2=10√3 kgms−1 along the y-axis These two momenta are perpendicular to each other. Therefore, the resultant initial momentum is Pi=√P21+P22=√(10)2+(10√3)2=20 kgms−1 If v is the velocity of the combined mass, then the final momentum, Pf=(10+5)v=15v. Now, from the principle of conservation of momentum, we have 15v=20⇒v=43 ms−1 Hence, the correct choice is (c).

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