A particle of mass m collides with a stationary particle and continues to move at an angle of 45° with respect to the original direction. The second particle also recoils at an angle of 45° to this direction. The mass of the second particle is (collision is elastic)
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Answers
Answer:
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Answer:
mass of the second particle is same as 1st particle i.e m
Explanation:
Given:- particle of mass of first particle 'm' collides and start moving at an angle 45°with Respect to original .
mass of 1st particle 'm'(given) let velocity u before collision and after collision mass m₀and velocity u₁
also suppose mass of second particle is M and velocity will be 0 (∵ stationary) before collision and after collision mass M₀and velocity v₀
coservation of momentum in horizantal direction.
∵ initial momentum = final momentum
∴ mu + M(0) = m₀u₀cos45° + Mₒv₀cos45°
⟹ mu = 1/√2 m₀u₀+ 1/√2Mₒv₀
⟹ mu = 1/√2(m₀u₀ + Mₒv₀) ______(1)
[conservation of momentum ]( In vertical axis )
- ∴ m₀u₀sin45°= Mₒv₀sin45°
- mₒu₀= M₀v₀_________(2)
[ ∵ it is elastic collision ∴e =1]
e = 1 = velocity of seperation /velocity of approach
1 = v₀-u₀cos90° /ucos45°
u/√2 = v₀
u = √2 v₀ _____(3)
from 1st , 2nd and (3)
m √2v₀ = 1/√2(2M₀V₀)
m = 2M₀/2= =M₀
- ∴ M₀ = m Answer
mass of the second particle is 'm'
