Tag: density and relative density

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Questions Related to density and relative density

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

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 ):

  1. 3 /4

  2. 4 /9

  3. 8 /15

  4. 9 /20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Newton's law of cooling states that the rate of heat loss is proportional to temperature difference, or time t is proportional to (mc / A). By setting up the ratio of times for identical volume, specific heat, and surface area conditions, the density ratio works out to 8/15.

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

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

  1. $\dfrac{\rho \omega^2 R^2}{2}$
  2. $\dfrac{\rho \omega^2 R}{2}$
  3. $\dfrac{\rho \omega R}{2}$
  4. $\dfrac{\rho^2 \omega^2 R^2}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a liquid cylinder of density rho rotates at angular speed omega, the pressure variation follows the hydrostatic equation dp/dr = rho omega^2 r. Integrating from the center (r = 0) to the radius R gives the pressure increase as Delta P = rho omega^2 R^2 / 2, making option A correct.

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.