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Question

# A solid cylinder of height h and mass m floats in a liquid of density ρ as shown in figure. Now the cylinder is released inside a liquid of density ρ4, contained in a downward accelerated vessel. Determine the magnitude of acceleration of vessel, a, for which cylinder sinks with relative acceleration a/3 with respect to vessel. Neglect any dissipative force :

A
23g
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B
43g
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C
34g
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D
13g
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Solution

## The correct option is A 23gVolume of cylinder=Vρ(34V)g=mgV=4m3ρIn reference frame of vesselmg−ρ4Vgeff−mA=mA3geff=g−Amg−ρ4(4m3ρ)(g-A)−mA=mA3or A=2g3

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