Question

A wooden cylinder of diameter 4r, height Hand density p/3 is kept on a hole of diameter 2r of a tank
filled with liquid of density p as shown in the figure,
level of the liquid stans decreasing slowly when the level of liquid is at a height h above the cylinder
the block starts moving up. At what value of h, will the block rise:
lIT-JEE 2006,5/184)
a: 4H/9
b:5H/9
c5H/3

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Answer 1

The block will rise when the value of H is 5H/3

Explanation:

Cross-section area of cylinder,

A1=π(2r)2=4πr2

Area of base cylinder in air,

A2=πr2

Area of base cylinder in water,

A3=4πr2−πr2=3πr2

The various forces acting on cylinder are shown in. As cylinder is in equililbrium, so

(P0+h1ρg)A1+ρ/3gHA1

=P0A2+[P0+ρgh1+ρgH]A3

On solving it gives

h1=5H/3

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