Tag: units - definitions and systems

Questions Related to units - definitions and systems

Which of the following is not the unit of surface tension ? 

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $newton/meter$

  2. $joule/(meter)^2$

  3. $kg/(second)^2$

  4. $watt/ meter$

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Correct Option: D

The Vander waal's equation for gas is given by $\left (P + \dfrac {a}{V^{2}}\right )(V - b) = RT$ where $P$ is pressure, $V$ is volume $'a'$ and $'b'$ are constants, $R$ is universal gas constant and $T$ is absolute temperature. Then the units of $'a'$ are

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $dyne\times cm^{5}$

  2. $dyne\times cm^{4}$

  3. $dyne\times cm^{3}$

  4. $dyne\times cm^{2}$

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Correct Option: B

Acceleration is defined as the rate of change of velocity. Unit of rate of change of acceleration is:

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $m/s^{2}$

  2. $m/s^{3}$

  3. $m/s$

  4. $m^{2}/s^{3}$

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Correct Option: B
Explanation:

Acceleration has unit $m/{s}^{2}$.

The rate of change of acceleration $\dfrac { d\overset { \rightarrow  }{ a }  }{ dt } =\dfrac { { d }^{ 3 }y }{ d{ t }^{ 3 } } =\dfrac { m }{ { s }^{ 3 } } $
Hence, option B is correct.

To express all the physical quantities in SI units, we need 

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. two fundamental units

  2. three fundamental units

  3. five fundamental units

  4. seven fundamental units

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Correct Option: D
Explanation:

SI unit system contains seven fundamental quantities which are independent to each other and can be used to represent any given quantity. Hence, all physical quantities can be represented in powers of seven fundamental SI units.

Which of the following quantity is unitless ?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. Velocity gradient

  2. Pressure gradient

  3. Displacement gradient

  4. Force gradient

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Correct Option: C
Explanation:

Gradient of a quantity $Q$ is given as $\dfrac{\Delta Q}{\Delta x}$
Thus, a gradient will be unitless if its numerator has same dimensions as denominator, i.e. $x$ (which has the dimension $L$).
Thus, out of the options, Displacement has the dimension $L$ and hence its gradient will be dimensionless.

In a system of units, the units of mass, length and time are called pail, jack, and jill. 1 pail = 5 kg, 1 m = 5 jacks and 24 s make 1 jill. What are the unit of density and speed in the new system?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $\displaystyle { (pails)\quad (jills) }^{ -2 }$

  2. $\displaystyle { (pails)\quad (jack) }^{ -3 }$

  3. $\displaystyle { (jack) }^{ 2 }(jill)$

  4. $\displaystyle { (pails)\quad (jack) }^{ 2 }$

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Correct Option: B
Explanation:

The unity of density$=\frac { unit\quad of\quad mass }{ { (unit\quad of\quad length) }^{ 3 } } \ =(pails){ (Jack) }^{ 3 }$

The value of $\displaystyle G=6.67\times { 10 }^{ -11 } N \ { m }^{ 2 } kg^{ -2 } and \ g={ 9.8ms }^{ -2 }$, what is the unit of g/G in C.G.S system?

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. $\displaystyle { g\quad cm }^{ -2 }$

  2. $\displaystyle { g\quad cm }^{ 2 }$

  3. $\displaystyle { g\quad cm }^{ -1 }$

  4. $\displaystyle { g\quad cm }$

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Correct Option: A
Explanation:
Unit of $g$ in SI is  $ms^{-1}$ and that of $G$ is $Nm^2 kg^{-2}$.
where  $1 \ N   = 1 \ kg \ ms^{-2}$ (in MKS system)

So, MKS units of $G$ is $m^3s^{-2}kg^{-1}$

Thus CGS unit of $g$ is  $cm \ s^{-2}$ and that of $G$ is $cm^3 s^{-2} g^{-1}$

Thus CGS unit of  $g/G$ is $g \ cm^{-2}$

The  SI unit of weight is.

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. kg wt

  2. N

  3. g wt

  4. all the above

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Correct Option: B
Explanation:

The weight of a body is , as the force with which the earth attracts it towards the centre.

$W= \dfrac{GMm}{R^2 }= mg$

$g$ (acceleration due to gravity) $= \dfrac{GM}{R^2}$

where,

$G$ is constant of gravitation, $R$ is distance from the centre if the earth, $M$ is the mass of the earth.

If the mass of the body $‘m'$ , the force of attraction of the earth or the $‘W'$ of the body is

$W= mg$

Weight is the force of attraction, its S.I. unit is same as that of S.I. unit of force .

The S.I. unit of weight is Newton (N).

The magnitude of a physical quantity consists of

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. a number and a unit

  2. a number

  3. a unit

  4. a unit and its symbol

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Correct Option: B
Explanation:

The magnitude of a physical quantity represent the amount contained in the quantity. Therefore, the magnitude of the quantity consists of a number only.


Option $B$ is correct.

If kg $m^2s^2$ represents 'x' and g $cm^2s^2$ represents 'y', then find the ratio of x to y.

physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

  1. 10$^7$

  2. 10$^5$

  3. 10$^9$

  4. 10$^3$

Show answer
Correct Option: A
Explanation:

We know that, 

$1 kg=1000g$
$1m=100cm$

Now, converting the unit $kg\ m^2\ s^2$ into $g\ m^2\ s^2$

$1\ kg\ m^2\ s^2=1000\ g\times(100\ m)^2\ s^2$

$=1000\times10^4\ g\ m^2\ s^2$
$=10^7 g\ cm^2\ s^2$