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Q.

A piston of mass M = 3kg and radius R = 4cm has a hole into which a thin pipe of radius 1 cm is inserted. The piston can enter the cylinder tightly and without friction and initially it is at the bottom of the cylinder. 750 gram of water is now poured into the pipe so that the piston and pipe are lifted up as shown. The height H of water in the cylinder is (Density of water is 103 kg/m3)

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a

1132π m

b

1332π m

c

1532π m

d

932π m

answer is A.

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Detailed Solution

(hρg)(A1 – A2) = Mgh ×103 ×π[(4 × 10-2)2 – (1 × 10-2)2] = 3 h×103×π15×10-4=3 h=2π[πr12H+πr22h]ρg=mg [π4×10-2 2H+π1×10-2 22π]1000=0.75 H=1132πm

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A piston of mass M = 3kg and radius R = 4cm has a hole into which a thin pipe of radius 1 cm is inserted. The piston can enter the cylinder tightly and without friction and initially it is at the bottom of the cylinder. 750 gram of water is now poured into the pipe so that the piston and pipe are lifted up as shown. The height H of water in the cylinder is (Density of water is 103 kg/m3)