Paragraph As seen in the figure, a long tall cylindrical body of density ρ= 3 gm/cc and radius r = 5 cm and length h = 20 cm moves along the axis of a vertical tall cylindrical vessel of radius R = 10

Question

Paragraph As seen in the figure, a long tall cylindrical body of density ρ= 3 gm/cc and radius r = 5 cm and length h = 20 cm moves along the axis of a vertical tall cylindrical vessel of radius R = 10 cm filled with liquid of density ρ 0 . Assume that there are no energy losses anywhere and ρ 0 = 1 gm/cc. The vessel is closed from top & bottom. What is the acceleration (in m / s 2 ) of the cylindrical body?

TestHub · Accepted Answer

A b o d y ​ = π r 2 , A l i q ​ = π ( R 2 − r 2 ) . A b o d y ​ a = A l i q ​ a ′ ⇒ a ′ = R 2 − r 2 r 2 ​ a m g − ρ 0 ​ V ( g + a ′ ) = ma m = ρ V : ρ g − ρ 0 ​ ( g + a ′ ) = ρ a ( ρ − ρ 0 ​ ) g = ρ a + ρ 0 ​ a ′ ( ρ − ρ 0 ​ ) g = a [ ρ + ρ 0 ​ R 2 − r 2 r 2 ​ ] a = ρ + ρ 0 ​ R 2 − r 2 r 2 ​ ( ρ − ρ 0 ​ ) g ​ a = 3 + 1 ⋅ 75 25 ​ ( 3 − 1 ) g ​ = 3 + 3 1 ​ 2 g ​ = 3 10 ​ 2 g ​ = 10 6 g ​ = 5 3 ​ g a = 6 m / s 2

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