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A particle with a mass of 0.3 kg moves rightward along the x-axis on a frictionless surface at 2 m/s. At x=0 it undergoes a completely elastic collision with a second particle of mass 0.4 kg, which is initially at rest. The second particle then moves rightward until it collides with a wall and rebounds. The second particle loses no speed after colliding with the wall. At what point on the x-axis does particle 2 collide with particle 1?

A particle with a mass of 0.3 kg moves rightward along the x-axis on a frictionless surface at 2 m/s. At x=0 it undergoes a completely elastic collision with a second particle of mass 0.4 kg, which is initially at rest. The second particle then moves rightward until it collides with a wall and rebounds. The second particle loses no speed after colliding with the wall. At what point on the x-axis does particle 2 collide with particle 1?

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Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
From conservation of linear momentum, the final velocities of bodies can be related as-
m_1v_0=m_2v_2-m_1v_1
Also since this is an elastic collision,v_1+v_2=v_0

Hence,v_1=\dfrac{2}{7}m/s
v_2=\dfrac{12}{7}m/s
Now time in which massm_2collides with wall and rebounds with same speed is\dfrac{0.7}{12/7}s=\dfrac{4.9}{12}s
Distancem_1has moved by then =\dfrac{2}{7}\times \dfrac{4.9}{12}m=\dfrac{0.7}{6}m
Separation between the particles at that time=\dfrac{0.7}{6}m+0.7m=\dfrac{4.9}{6}m
Relative speed of the the two particles=\dfrac{12}{7}-\dfrac{2}{7}=\dfrac{10}{7}m/s

Hence the time in which the particles meet=\dfrac{\dfrac{4.9}{6}}{\dfrac{10}{7}}=\dfrac{343}{600}s

Hence the distance of the point from the wall= Distance travelled by massm_2
=\dfrac{343}{600}s\times \dfrac{12}{7}m/s=\dfrac{49}{50}m=98cm

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