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Question

# In a cylindrical container, open to the atmosphere from the top, a liquid is filled upto 10 m depth. Density of the liquid varies with depth from the surface as ρ(h)=100+6h2 where h is in meter and ρ is in kg/m3. The pressure at the bottom of the container will be: (atmospheric pressure = 105Pa, g=10m/sec2)

A
1.7×105Pa
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B
1.4×105Pa
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C
1.6×105Pa
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D
1.3×105Pa
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Solution

## The correct option is D 1.3×105Padp=ρgdh∫P=PfP=P0=∫h=10h=0(100+6h2)gdhPf−P0=(1000h+20h3)h=10h=0⇒Pf=105+0.3×105=1.3×105Pa

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