Tag: upthrust in fluids, archimedes' principle and floatation

Questions Related to upthrust in fluids, archimedes' principle and floatation

By cooling two liquids of equal volume from temperature $60 ^ { \circ } \mathrm { C }$  to $50 ^ { \circ } \mathrm { C }$ in same conditions time required are 324 and 810 sec respectively. If ratio of specific heat of both are 3:4. Then ratio of their. densities (water equivalent of calorimeter is negligible ):

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. 3 /4

  2. 4 /9

  3. 8 /15

  4. 9 /20

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Correct Option: A

The density of water at $4^oC$ in S.I. unit is $X\ kg m^{-3}$. Find $\dfrac{X}{250}$

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: D
Explanation:

Density of water at $4^{\circ}C$ in S.I. unit is $1000 kgm^{-3}$.

Hence, value of $X=1000$ 
$\therefore\dfrac{X}{250}=4$

The density of wood is 0.65 $ \displaystyle g\ cm^{3} $ in CGS system. Its density in SI system is

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. 65 $ \displaystyle kgm^{3} $

  2. 6.5 $ \displaystyle kgm^{3} $

  3. 650 $ \displaystyle kgm^{3} $

  4. 0.65 $ \displaystyle kgm^{3} $

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Correct Option: C
Explanation:

As 1 gm per cc  = 1000 kg per mc

so 0.65 gm per cc = 0.65 (1000) kg per mc = 650kg per mc       ( where cc = centimetre cube) and mc = metre cube)
hence option (C) is correct

A sphere is dropped under gravity through a fluid of viscosity $h$. If the average acceleration is half of the initial acceleration, the time to attain the terminal velocity is $(r=density\ of\ sphere,r=radius)$

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $\dfrac{4\rho r^{2}}{9 \eta}$

  2. $\dfrac{5\rho r}{9 \eta}$

  3. $\dfrac{4\rho r}{9 \eta}$

  4. $\dfrac{9\rho r}{9 \eta}$

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Correct Option: A

The unit of density in MKS and CGS system respectively are:

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $\displaystyle { kg }/{ { m }^{ 3 } }and\quad { g }/{ { cm }^{ 3 } }$

  2. $\displaystyle { g }/{ { cm }^{ 3 } }and\quad { kg }/{ { m }^{ 3 } }$

  3. $\displaystyle { g }/{ { cm }^{ 2 } }and\quad { kg }/{ { m }^{ 2 } }$

  4. $\displaystyle { kg }/{ { cm }^{ 2 } }and\quad { g }/{ { m }^{ 2 } }$

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Correct Option: A
Explanation:

Density is defined as the mass per unit volume of a substance. 

Density = $\cfrac{mass}{volume}$. 
In MKS system i.e. the SI system the unit of density is $\displaystyle { kg }/{ { m }^{ 3 } }$ and CGS system it is $\displaystyle { g }/{ { cm }^{ 3 } }$.

$1\ kg/m^3$ is equal to

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $10^3\ g/cm^3$

  2. $1\ g/cm^3$

  3. $10^{-3}\ g/cm^3$

  4. None of the above

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Correct Option: C
Explanation:

$1\ kg/m^3 = 10^3g/10^6cm^3=10^{-3}g/cm^3$

A cylinder of radius R full of liquid of density $\rho$ is rotated about its axis at $\omega$ rad/s. The increase in pressure at the centre of the cylinder will be

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $\dfrac{\rho \omega^2 R^2}{2}$

  2. $\dfrac{\rho \omega^2 R}{2}$

  3. $\dfrac{\rho \omega R}{2}$

  4. $\dfrac{\rho^2 \omega^2 R^2}{2}$

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Correct Option: B

Two solids A and B having same volume float in water. It is observed that A floats with half its volume immersed and B floats with $1/3^{rd}$ of its volume immersed. Compare the densities of A and B.

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $4: 3$

  2. $2: 3$

  3. $3: 4$

  4. $1: 3$

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Correct Option: C

Equal masses of three liquid are kept in there identical cylindrical vessels $A, B$ and $C$. There densities are $\rho _{A}, \rho _{B}$ and $\rho _{C}$ with $\rho _{A} < \rho _{B} < \rho _{C}$. The force on the base will be

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. Maximum in vessel $A$

  2. Maximum in vessel $B$

  3. Maximum in vessel $C$

  4. Same in all the three vessel

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Correct Option: D
Explanation:

Since masses are same,(weight$=mg$) is same for all three.

The value of $g$ on the surface of earth is 9.8 $m / s ^ { 2 }$ and the radius of earth is $6400km$. The average density of earth in $k g / m ^ { 3 }$ will be

physics upthrust in fluids, archimedes' principle and floatation density of a fluid density of fluid density and relative density

  1. $5.48 \times 10 ^ { 3 }$

  2. $2.64 \times 10 ^ { 3 }$

  3. $7.60 \times 10 ^ { 3 }$

  4. $1.46 \times 10 ^ { 3 }$

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Correct Option: A