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Question

A wooden block is floating in a liquid. About 50% of its volume is inside the liquid when the vessel is stationary. Percentage volume immersed when the vessel moves upwards with acceleration a=g2 is

A
75%
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B
25%
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C
50%
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D
33.33%
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Solution

The correct option is C 50%
When the vessel is stationary
weight=upthrustVρwg=VρlgVV=ρwρl..........(I)ρw=density of wood;ρl=density of liquid
When the vessel moves upward with an acceleration g2
upthrustweight=mass×accelerationV′′(g+g2)ρlVρwg=Vρwg232(V′′ρlg)=32(Vρwg)V′′V=ρwρl..........(II)
From equation (I) and (II), We have V=V′′ Fraction of the volume immersed remains unchanged i.e. 50%.

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