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

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

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

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

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

  4. 0.65 $ \displaystyle kgm^{3} $
Reveal answer Fill a bubble to check yourself
C Correct answer
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

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

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 $(r=density\ of\ sphere,r=radius)$

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

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

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

  4. $\dfrac{9\rho r}{9 \eta}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The time to attain terminal velocity is related to the relaxation time of the sphere in the fluid. Based on the equation of motion for a sphere in a viscous fluid, the characteristic time constant is 2/9 * (rho * r^2 / eta). Given the acceleration condition, the result is 4/9 * (rho * r^2 / eta).

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

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

  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. $\displaystyle { kg }/{ { cm }^{ 2 } }and\quad { g }/{ { m }^{ 2 } }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\displaystyle { g }/{ { cm }^{ 3 } }$.

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

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

  1. Maximum in vessel $A$

  2. Maximum in vessel $B$

  3. Maximum in vessel $C$

  4. Same in all the three vessel
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

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

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

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

  4. $1.46 \times 10 ^ { 3 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using g = G * M / R^2 and M = density * (4/3) * pi * R^3, we get g = G * density * (4/3) * pi * R. Solving for density = 3g / (4 * pi * G * R). Plugging in g=9.8, G=6.67e-11, R=6.4e6, we get approx 5.48e3 kg/m^3.

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

The equation $\alpha =\dfrac { D-d }{ (n-1)d } $ is correctly matched for :
Where D= Theoretical vapour density
            d= Observed vapour density 

  1. $A\rightleftharpoons \dfrac { nB }{ 2 } +\dfrac { nC }{ 3 } $

  2. $A\rightleftharpoons \dfrac { nB }{ 3 } +\dfrac { 2n }{ 3 } C$

  3. $A\rightleftharpoons \left(\dfrac { n }{ 2 } \right)B+\left(\dfrac { n }{ 4 } \right)C$

  4. $A\rightleftharpoons \left(\dfrac { n }{ 2 } \right)B+C$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The degree of dissociation alpha = (D-d) / ((n-1)d) corresponds to the dissociation reaction A -> nB + ... where the total number of moles increases by (n-1). Option A represents a reaction where the stoichiometry leads to this specific expression.