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Question

# Two bodies of mass 0.4 kg and 0.8 kg move towards each other with initial velocities 5 m/s and 2 m/s respectively. After the collision, they stick together. Then, find the distance travelled by the combined mass, 12 sec after the collision.

A
3 m
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B
12 m
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C
8 m
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D
4 m
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Solution

## The correct option is D 4 mLet m1=0.4 kg, m2=0.8 kg The initial velocities of bodies before collision are v1=+5 m/s, v2=−2 m/s as shown in figure. After the collision, masses stick together, so combined mass is (m1+m2). Let the masses move with common velocity v. Applying conservation of linear momentum on system of bodies: Pi=Pf m1v1+m2v2=(m1+m2)v ⇒(0.4)(+5)+(0.8)(−2)=(1.2)v ∴v=0.41.2=13 m/s Hence, the combined system moves with velocity v in the initial direction of motion of 0.4 kg mass. ⇒Distance travelled by combined mass in time interval t=12 sec, after collision is d=v×t=13×12=4 m

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