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Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively. If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then:

  1. P floats in A and Q sinks in B

  2. P sinks in A and Q floats in B

  3. P floats in B and Q sinks in A

  4. P sinks in B and Q floats in A
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If solid object has higher density than liquid then it will sink in that liquid otherwise it will float.
R.D. of liquid A = 0.75
R.D. of liquid B = 1.0
R.D. of object P = 0.6
R.D. of object Q = 0.9

  • P has R.D. less then both the liquids. so it will float in both the liquids.
  • Q has R.D. more than liquid A, so it will sink in A.
  • Q has R.D. less than liquid B, so it will float in B.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A metallic wire of length, "l" is lying horizontally on the surface of liquid of density $ '\rho' $ The maximum radius of wire so that it may not sink will be

  1. $ \sqrt { \frac { 2T }{ \pi \rho g } } $

  2. $ \sqrt { \frac { T }{ \pi \rho g } } $

  3. $ \sqrt { \frac { 2T }{ \rho g } } $

  4. $ \sqrt { \frac { T }{ \rho g } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A cube of wood supporting a $200$ gm mass just floats in water. When the mass is removed the cube rises $2$ cm at equilibrium. Find size of the cube.

  1. 10cm

  2. 12cm

  3. 15cm

  4. 4cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The weight of the 200g mass equals the weight of the water displaced by the additional 2cm immersion. 200g = (Area * 2cm) * density_water. Area = 100 cm^2. Side length = 10 cm.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A wire of length $L$ metrs, made of a material of specific gravity $8$ is floating horizontally on the surface of water. If it is not wet by water, the maximum diameter of the wire (in mm) up to which it can continue to float is (surface tension of water is) ($T=70\times 10^{-3} \ N/m$)

  1. $1.5$

  2. $1.1$

  3. $0.75$

  4. $0.55$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The weight of the wire (pi * r^2 * L * rho_wire * g) is balanced by surface tension (2 * T * L). Solving for diameter d = 2r: pi * (d/2)^2 * rho_wire * g = 2 * T. Plugging in values gives d approximately 1.5 mm.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A hollow cylinder of copper of length $25\, cm$ and area of cross-section $15\, cm^2$, floats in water with $3/5$ of its length inside water. Then 

  1. Apparent density of hollow copper cylinder is $0.6\, gcm^{-3}$

  2. Weight of the cylinder is $225\, gf$

  3. Extra force required to completely submerge it in water is $150\, gf$

  4. Extra force required to completely submerge it in water is $225\, gf$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Weight of the cylinder = buoyant force = (3/5 * 25 cm * 15 cm^2) * 1 g/cm^3 = 225 gf. This confirms option B.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

Two solids $A$ and $B$ float in water. It is observed that $A$ floats with half its volume immersed and $B$ floats with $\dfrac{2}{3}$ of its volume immersed. Compare the densities of A and B.

  1. $4:3$

  2. $2:3$

  3. $3:4$

  4. $1:3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a floating object, density_object / density_fluid = fraction_submerged. Density_A / Density_water = 1/2. Density_B / Density_water = 2/3. Ratio A:B = (1/2) / (2/3) = 3/4.