A uniform disc of radius R is put over another uniform disc of radius 2R of the same thickness and density. The peripheries of the two discs touch each other. Locate the center of the mass of the system.
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ANSWER::
See figure for better understanding.
Lets assume the centre of the bigger disc to be the origin.
Radius of bigger disc = 2R
Radius of smaller disc = R
m₁=πR² x T x ρ x₁=R y₁=0
m₂=π(2R)² x T x ρ x₂=0 y₂=0
where as ,
T = Thickness of both discs
ρ = Density of both discs
Position of centre of mass =
[(m₁x₁+m₂x₂)/(m₁+m₂) , (m₁y₁+m₂y₂)/(m₁+m₂)]
= [(πR²TρR + 0) / (πR²Tρ + π(2R)²Tρ ) , 0 / (m₁+m₂)]
= [(πR²TρR) / (5πR²Tρ) , 0 ]
= (R/5 , 0)
Hope it helps!
ANSWER::
See figure for better understanding.
Lets assume the centre of the bigger disc to be the origin.
Radius of bigger disc = 2R
Radius of smaller disc = R
m₁=πR² x T x ρ x₁=R y₁=0
m₂=π(2R)² x T x ρ x₂=0 y₂=0
where as ,
T = Thickness of both discs
ρ = Density of both discs
Position of centre of mass =
[(m₁x₁+m₂x₂)/(m₁+m₂) , (m₁y₁+m₂y₂)/(m₁+m₂)]
= [(πR²TρR + 0) / (πR²Tρ + π(2R)²Tρ ) , 0 / (m₁+m₂)]
= [(πR²TρR) / (5πR²Tρ) , 0 ]
= (R/5 , 0)
Hope it helps!
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