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Standard XII

Physics

Wave Equation

For a cylinde...

Question

For a cylinder of density $1.5 g c m^{- 3}$ , buoyant force is $4$ N inside a liquid of density d. Find the buoyant force on the same cylinder inside a liquid of density $3$ d.

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Solution

$d = 1.5 g c m^{- 3}, F B_{1} = 4 N$
$d_{L 1} = d, F B_{2} = ?, d_{L 2} = 3 d$
We know,
$F B α d_{1}$
$\Rightarrow \frac{F B_{1}}{F B_{2}} = \frac{d_{L 1}}{d_{L 2}}$
$\Rightarrow F B_{2} = \frac{F B_{1} \times d_{L 2}}{d_{L 1}} = \frac{4 \times 3 d}{d} = 12 N$

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Similar questions

Q. A cylinder made up of a material of density

1.5 g c m^{- 3}

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Column I Column II

i. Net force on cylinder from liquid-1	1. Zero
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iii. Density of solid ( $ρ_{s}$ )	3. Net upthrust
iv. Buoyant Force	4. $ρ_{s} g A$ ( $h_{1}$ + $h_{2}$ + $h_{3}$ )
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Fill in the blank:

The buoyant force exerted by a liquid _______ with the decrease in density of liquid.

A solid cylinder of height h and mass m floats in a liquid of density $ρ$ as shown in Fig. Now the cylinder is released inside a liquid of density $\frac{ρ}{4}$ , contained in a downward accelerated vessel. Determine the magnitude of acceleration of vessel(A), for which cylinder sinks with relative acceleration $\frac{A}{3}$ with respect to vessel.
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For a cylinder of density 1.5gcm−3, buoyant force is 4 N inside a liquid of density d. Find the buoyant force on the same cylinder inside a liquid of density 3d.

d=1.5gcm−3,FB1=4NdL1=d,FB2=?,dL2=3dWe know,FBαd1⇒FB1FB2=dL1dL2⇒FB2=FB1×dL2dL1=4×3dd=12N

For a cylinder of density $1.5 g c m^{- 3}$ , buoyant force is $4$ N inside a liquid of density d. Find the buoyant force on the same cylinder inside a liquid of density $3$ d.

$d = 1.5 g c m^{- 3}, F B_{1} = 4 N$
$d_{L 1} = d, F B_{2} = ?, d_{L 2} = 3 d$
We know,
$F B α d_{1}$
$\Rightarrow \frac{F B_{1}}{F B_{2}} = \frac{d_{L 1}}{d_{L 2}}$
$\Rightarrow F B_{2} = \frac{F B_{1} \times d_{L 2}}{d_{L 1}} = \frac{4 \times 3 d}{d} = 12 N$