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Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

A body of density $\rho$ is dropped from rest from a height h into a lake of density $\sigma$, where $\sigma > \rho$. Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface

  1. $\dfrac{h}{\sigma - \rho}$
  2. $\dfrac{h\rho}{\sigma}$
  3. $\dfrac{h\rho}{\sigma - \rho}$
  4. $\dfrac{h\sigma}{\sigma - \rho}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

${V _f}^2-V _1^2=2as$

$\Rightarrow r-(2gh)=2 \times -\left(\cfrac {\sigma}{\delta}-1\right)g \times s$
$\Rightarrow s=\left(\cfrac {h}{\cfrac {\sigma}{\delta}-1}\right)$
$\Rightarrow \left[s=\cfrac {h\rho}{\sigma-\rho}\right]$

Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

A sphere of iron and another of wood, both of same radius are placed on the surface of water. State which of the two will sink? (It is given $\rho _{iron} > \rho _{water}$, and  $\rho _{wood} < \rho _{water}$)

  1. Sphere of iron will sink.

  2. Sphere of wood will sink.

  3. both will sink

  4. both will not sink
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since density of iron is more than that of wood, so weight of iron sphere will be more than upthrust due to water on it. But density of wood is less than that of iron so sphere of wood will float. 

Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

How does the density of a substance determine whether a solid piece of density $\rho _s$ of that substance will float or sink in a given liquid of density $\rho _L$?

  1. The body will float if $\rho _s \leq \rho _L$ and it will sink if $\rho _s < \rho _L$.
  2. The body will float if $\rho _s \leq \rho _L$ and it will sink if $\rho _s > \rho _L$.
  3. The body will float if $\rho _s > \rho _L$ and it will sink if $\rho _s > \rho _L$.
  4. The body will float if $\rho _s > \rho _L$ and it will sink if $\rho _s < \rho _L$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The body will float if $\rho _{s}$ < $\rho _{L}$ and it will sink if $\rho _{s}$ > $\rho _{L}$
If the density of the substance is less than the density of the liquid, then the substance will float in liquid.
If the density of the substance is greater than the density of the liquid, then the substance will sink in liquid.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

The dimensions of a wooden raft (density $ =150\ kg/ m^3)$ are $3.0\ m\times 3.0\ m\times 1.0\ m$. What maximum load can it carry in seawater so that the plank just floats in water (density$=1020\ kg/m^3)$?

  1. $1350\ kg$
  2. $7830\ kg$
  3. $9200\ kg$
  4. $19,500\ kg$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object.

Buoyancy force can be calculated with the equation 
$Fb=Vs\times D\times g$

where $F _b$ is the buoyancy force, $V _s$ is the submerged volume, $D$ is the density of the fluid the object is submerged in, and $g$ is the force of gravity.

It can also be given as the sum of the weight of the raft and the weight of the load. That is, ${ W } _{ raft }+{ W } _{ load }$ = $Fb=Vs\times D\times g$.

The weight of the raft
${ W } _{ raft }={ V } _{ raft }{ D } _{ raft }g$.

At maximum load, Volume of water displaced is equal to volume of the raft.

${ max(W } _{ load })=({ D } _{ water }-{ D } _{ raft }){ V } _{ raft }g$.
=$(1020kg/{ m }^{ 3 }-150kg/{ m }^{ 3 })(3m\times 3m\times 1m)g$
$=7830 kg.$

Hence, the maximum load the raft can carry sea water so that the plank just floats in water is $7830 kg.$
Multiple choice physics upthrust in fluids, archimedes' principle and floatation experimental verification of archimedes' principle archimedes' principle archimedes' principle and its applications

Two unequal blocks place over each other of different densities ${ \sigma  } _{ 1 }$ and ${ \sigma  } _{ 2 }$ are immersed in fluid of density of $\sigma$. The block of density ${ \sigma  } _{ 1 }$ is fully submerged and the block of density ${ \sigma  } _{ 2 }$ is partly submerged so that ratio of there masses is $1/2$ and $\sigma/{ \sigma  } _{ 1 }=2$ and $\sigma/{ \sigma  } _{ 2 }=0.5$. Find the degree of submergence of the upper block of density ${ \sigma  } _{ 2 }$.

  1. $50\%$ submerged
  2. $25\%$ submerged
  3. $75\%$ submerged

  4. Fully submerged
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the equilibrium condition for floating bodies and the given ratios, the forces balance such that the upper block is fully supported by the buoyancy of the lower block and its own displacement.

Multiple choice physics life cycle of stars movement of the earth properties of stars types of galaxies

Mass (in kg) of the massive object at the centre of the milky way galaxy is of the order.

  1. $10 ^ { 32 }$
  2. $10 ^ { 37 }$
  3. $10 ^ { 43 }$
  4. $10 ^ { 29 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The supermassive black hole at the center of the Milky Way, Sagittarius A*, has a mass estimated to be approximately 4 million solar masses. One solar mass is about 2 x 10^30 kg, so 4 x 10^6 * 2 x 10^30 = 8 x 10^36 kg, which is of the order 10^37.

Multiple choice physics life cycle of stars movement of the earth properties of stars types of galaxies

A galaxy that is moving toward the Earth will show:

  1. a red shift in the spectrum

  2. an increase in light years

  3. a decrease in brightness

  4. a blue shift in the spectrum
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As galaxy move towards the earth the wavelength decreases and the frequency increase and colour changes to blue and also known as blue shift while opposite is known as red shift.

Multiple choice physics life cycle of stars movement of the earth properties of stars types of galaxies

The red shift in the spectral lines of light reaching us from other galaxies implies that these galaxies:

  1. are moving closer to one another

  2. are moving farther apart from one another

  3. consist predominantly of red giant stars

  4. are in rapid rotation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The red shift occurs due to increase due to increase in wavelength that would be due to the increasing distance between two galaxies, Red shift indicate that galaxy are mainly farther apart from one another