A mass M, attached to a horizontal spring excutes SHM with amplitude A₁ . When the mass M pases through its mean position , then a smaller mass m is placed over it and both of them move together with amplitude A₂ . The ratio of (A₁/A₂) is [AIEEE 2011 ]
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Answer:
. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A
2
. The ratio of (
A
2
A
1
)
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ANSWER
Velocity of particle at mean position initially,
V
′
=ωA
1
V
′
=
M
K
A
1
→(1)
After placing another mass,
(m+M)V
′′
=MV
′
V
′′
=
(m+M)
MV
′
V
′′
=ω
′
A
2
V
′′
=
m+M
K
A
2
M+m
MV
′
=
m+M
K
A
2
→(2)
ondividingboth,
M
M+m
=
M
M+m
A
2
A
1
A
2
A
1
=(
M
M+m
)
2
1
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6
Explanation:- At mean position ,Fnet = 0
- ∴ By conservation of linear momentum
- Mv₁ = (M+m)V₂
- Mω₁A₁ = (M+m)ω₂A ₂
But , angular velecity ,
- ω ₁ = √k/M
- ω₂ = √k/(M+m)
- On solving
A₁/A₂ = (Μ+m)ω₂/(M)ω₁
A₁/A₂ =[( M+m)/M)]^½ Answer .
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