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

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

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

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

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

  4. $dyne\times cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In the equation (P + a/V^2)(V - b) = RT, the term a/V^2 must have the same units as pressure P. Thus, units of a = units of P * units of V^2. Pressure is force/area (dyne/cm^2 in CGS) and volume is length^3 (cm^3). So, a = (dyne/cm^2) * (cm^3)^2 = dyne * cm^4.

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

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

  1. $m/s^{2}$

  2. $m/s^{3}$

  3. $m/s$

  4. $m^{2}/s^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. two fundamental units

  2. three fundamental units

  3. five fundamental units

  4. seven fundamental units
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

Which of the following quantity is unitless ?

  1. Velocity gradient

  2. Pressure gradient

  3. Displacement gradient

  4. Force gradient
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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?

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

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

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

  4. $\displaystyle { (pails)\quad (jack) }^{ 2 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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?

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

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

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

  4. $\displaystyle { g\quad cm }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $g \ cm^{-2}$
Multiple choice physics motion and measurement physical quantities units - definitions and systems physical quantities like mass and weight

The  SI unit of weight is.

  1. kg wt

  2. N

  3. g wt

  4. all the above
Reveal answer Fill a bubble to check yourself
B Correct answer
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).

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

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

  1. 10$^7$

  2. 10$^5$

  3. 10$^9$

  4. 10$^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that, 

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

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

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

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

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

State whether true or false.
The measure of an angle is dependent upon the unit of length.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Plane angle is defined as the ratio of arc length to the radius.
Plane angle   $\theta = \dfrac{l}{r}$
So, the measure of an angle is dependent upon the unit of length. Thus, the given statement is true.