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Question

Two smooth spheres made of identical material having masses m and 2m undergo an oblique impact as shown in figure. The initial velocities of the masses are also shown. The impact force is along the line joining their centres. The coefficient of restitution is 5/9. The velocities of the masses after the impact are:


A
103^i+8j,53^i+43j,
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B
53^i8j,53^i+4j,
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C
103^i8^j,53^i+4^j,
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D
None of these
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Solution

The correct option is C 103^i8^j,53^i+4^j,
Velocity components before collision


Line of impact is along x-axis. Hence, velocities perpendicular to the x-axis remain unchanged.
Hence y component velocity after collision
For A:
vAy=10sin53^j=10×45^j=8^j
For B:
vBy=5sin53=5×45^j=4^j

x - component of velocities after collision.
By momentum conservation (because no external force is present)
2m(5cos53)m×(10cos53)=2m vBx+mvAx
2vBx+vAx=0 ...(I)

As we know, e=velocity of seperationvelocity of approach in horizontal direction
i.e e=vAxvBx5cos53+10cos53=59
or vAxvBx=5 ...(II)

From eq. (I) and (II) vAx=103 vBx=53
Hence, after collision,
Velocity of sphere A,vA=103^i8^j
Velocity of sphere B,vB=53^i+4^j

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