Tag: fundamental quantities

Questions Related to fundamental quantities

If the volume of a cube is equal to its surface area in magnitude. Then the volume of the cube is? 

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $216$ unit

  2. $512$ unit

  3. $64$ unit

  4. None of these

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Correct Option: A
Explanation:

Let us take side of cube$=a$
then  $a^3=6a^2$
$\therefore a=6$
So volume of cube is:

$a^3=(6)^3=216$ units

In the eqn. $\left (P+\dfrac {a}{V^2}\right )(V-b)=$ constant, the unit of $a$ is

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $dyne\times cm^5$

  2. $dyne\times cm^4$

  3. $dyne/cm^3$

  4. $dyne\times cm^2$

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Correct Option: B
Explanation:

Units of both $P $ and $ \dfrac {a}{V^2}$ must be same.
So, $\dfrac {a}{V^2}=P$  $\implies   a=PV^2$ 

Since unit of $P$ is $dyne \ cm^{-2}$ and that of $V$ is $cm^3$.
$\therefore$ Unit of a is  $\dfrac {dyne}{cm^2}(cm^3)^2=dyne\times cm^4$

Unit of specific resistance is

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $\Omega/m^2$

  2. $\Omega m^3$

  3. $\Omega m$

  4. $\Omega/m$

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Correct Option: C
Explanation:

Specific resistance of a material is given by

$\rho =\displaystyle \frac {RA}{l}$

Substitute the unit in the above expression:
$\rho=\dfrac {\Omega.m^2}{m}=\Omega m$

Which of the following is different from others?

physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

  1. Speed

  2. Density

  3. Force

  4. Time

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Correct Option: D
Explanation:

Speed, density and force are the derived physical quantities whereas time is the fundamental physical quantity.

Mass is a _________ physical quantity.

physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

  1. derived

  2. fundamental

  3. semi-derived

  4. valueless

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Correct Option: B
Explanation:

There are only $7$ fundamental physical quantity out of which mass is a fundamental quantity.

Which of the following physical quantity is different form others ?

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. Displacement

  2. Velocity

  3. Force

  4. Kinetic energy

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Correct Option: D
Explanation:

Displacement, force, and velocity are vector quantities as they require direction as well as the magnitude for their representation but the kinetic energy is a scalar quantity as it does not require direction for its representation.

Write the SI unit of the physical quantity having following dimensional formula
$\displaystyle [{ M }^{ 0 }{ L }^{ 2 }{ T }^{ -2 }{ K }^{ -1 }]$.

physics measurements and units kinds of units fundamental quantities standardized measurement

  1. $\displaystyle {m} { kg }^{ 2 }{ K }^{ -1 }$

  2. $\displaystyle {m} ^{2} { kg }^{ 2 }{ T }^{ -1 }$

  3. $\displaystyle {m} ^{2} { s }^{ -2 }{ K }^{ -1 }$

  4. $\displaystyle {m} ^{2} { kg }^{ 2 }{ K }^{ -1 }$

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Correct Option: C
Explanation:
SI unit of $M$ is $kg$, that of $L$ is $m$, $T$ is $s$ and temperature (K) is $K$.

So, SI unit of $[M^0L^2T^{-2}K^{-1}]$ is  $m^2s^{-2}K^{-1}$.

Dimensional analysis is the analysis of the relationships between different physical quantities by 

physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

  1.  identifying their fundamental dimensions

  2. units of measure

  3. tracking these dimensions as calculations or comparisons are performed.

  4. All of the above 

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Correct Option: D
Explanation:

Dimensional analysis establishes the relation between the physical quantities by comparing the different quantities using their fundamental dimensions.

The dimensional analysis also makes use of the units to measure different quantities and the dimensional analysis is also helpful in performing several calculations.

State whether true or false.
The mass of a body can never be zero.

physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

  1. True

  2. False

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Correct Option: A
Explanation:
Mass of a body is defined as the quantity of matter contained in it. Since, all bodies are made up of certain matter. Thus mass of body can never be zero.

Which one of the following is not a fundamental SI unit?

physics measurement of physical quantities kinds of units fundamental quantities standardized measurement

  1. Ampere

  2. Candela

  3. Newton

  4. Kelvin

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Correct Option: C
Explanation:

F = ma = kgms-2

SI unit of force is Newton(W)

Hence, newton is a derived unit