Units and Measurements Test

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Units and Measurements Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

The dimensional formula for moment of couple is :

A
$$[{ M }^{ 1 }{ L }^{ 2 }{ T }^{ -1 }]$$

B
$$[{ M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 }]$$

C
$$[{ M }^{ -1 }{ L }^{ 2 }{ T }^{ -2 }]$$

D
$$[{ M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 }]$$

Solution

Moment of a couple is calculated by multiplying the size of one of the force (F) by the perpendicular distance between the two forces.
Thus the units are that of $$Nm$$ and dimensions are $$[(M^{1}LT^{-2})(L)]=[M^{1}L^2T^{-2}]$$
Question 2
1 / -0

The measure of accuracy is :

A
absolute error

B
relative error

C
percentage error

D
Both B and C

Solution

$${\textbf{Explanation:}}$$
$$\bullet$$ Accuracy is measured as the deviation from true reading compared with the observed reading. Accuracy of a measured value tells how close the measured value is to the actual value.
$$\bullet$$ Absolute error is the deviation of a reading from the actual or true reading.
$$\bullet$$ Relative error is defined on true error, as the difference of a value of the true or actual value divided by the actual value.
$$\bullet$$ Whereas percentage error is expressed in terms of percentage, i.e. by multiplying the relative error by 100, it is called percentage error. Both relative and percentage error give a quantitative analysis of the deviation from the true value.
$$\bullet$$ For example in 2 separate experiments with true value 1000m and 1m have absolute error as 0.1m. Now the relative error in these cases will be 0.999 and 0.9. So absolute error fails to tell us the correct measure of accuracy and relative or percentage error takes the win.

$${\textbf{Correct option: D}}$$
Question 3
1 / -0

If the unit of tension is divided by the unit of surface tension the derived unit will be same as that of

A
mass

B
length

C
area

D
work

Solution

Tension $$= M^{1} L^{1} T^{-2}$$
Surface Tension $$\displaystyle = \frac{f}{l} = \frac{M^{1} L^{1} T^{-2}}{L^{1}} = M T^{-2}$$
$$\displaystyle \frac{Tension}{Surface Tenstion} = \frac{M^{1} L^{1} T^{-2}}{M T^{-2}} = L^{1}$$
Question 4
1 / -0

$$\left[ \dfrac { Permeability }{ Permittivity } \right] $$will have the dimensions of :

A
$${ M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 }{ A }^{ 0 }$$

B
$${ M }^{ 2 }{ L }^{ 2 }{ T }^{ 4 }{ A }^{ 2 }$$

C
$${ M }^{ 2 }{ L }^{ 4 }{ T }^{ -6 }{ A }^{ -4 }$$

D
$${ M }^{ -2 }{ L }^{ -4 }{ T }^{ 6 }{ A }^{ 4 }$$

Solution

Permeability $$= \mu _{0} = M L A^{-2} T^{-2}$$ .........(1)
Permittivity $$= M^{-1} L^{-3} A^{2} T^{4}$$ .................(2)
So, $$\dfrac{eq^{n}(1)}{eq^{n}(2)} = \dfrac{M L A^{-2} T^{-2}}{M^{-1} L^{-3} A^{2} T^{4}} = M^{2} L^{+4} A^{-4} T^{-6}$$
Hence, option C is correct.
Question 5
1 / -0

Which of the following is/are dimensionless ?
a) Boltzman’s constant b) Planck’s constant c) Poisson’s ratio d) Relative constant

A
a and b

B
c and b

C
c and d

D
d and a

Solution

Poisson's ratio is ratio of young modulus, hence dimensionless.
Relative constant is also a constant.
Boltzman's constant $$=M^{1}L^{2}T^{-2}K^{-1}$$
Plancks constant $$=ML^{2}T^{-1}$$
Hence, option C is correct.
Question 6
1 / -0

The fundamental unit which has the same power in the dimensional formula of surface tension and coefficient of viscosity is:

A
mass

B
length

C
time

D
none

Solution

Surface tension $$= \dfrac{F}{l} = \dfrac{M^{1}L^{1}T^{-2}}{L^{1}} = M^{1}T^{-2}$$
Coeff of viscosity $$= \dfrac{k}{qA\dfrac{dv}{dz}} = \dfrac{M^{1}L^{1}T^{-2}}{\dfrac{L^{2}LT^{-1}}{L}} = M^{1}L^{-1}T^{-1}$$
Hence, mass has the same power.
Question 7
1 / -0

If $$\mu $$ is the permeability and $$\epsilon $$ is the permittivity then $$\dfrac { 1 }{ \sqrt { \mu \epsilon } } $$ is equal to

A
speed of sound

B
speed of light in vacuum

C
speed of sound in medium

D
speed of light in medium

Solution

We know that speed of light in vacuum $$c=\dfrac{1}{\sqrt{\mu_0\epsilon_0}}=\dfrac{1}{\sqrt{(4\pi\times 10^{-7})(8.314\times 10^{-12})}}\sim 2.98\times 10^8 m/s$$
Thus, $$\dfrac{1}{\sqrt{\mu\epsilon}}$$ will also represent the speed of light in a medium whose permittivity is $$\epsilon$$ and permeability, $$\mu$$.
Question 8
1 / -0

The physical quantity having the same dimensional formula as that of entropy is:

A
Latent heat

B
Thermal capacity

C
Heat

D
Specific heat

Solution

Entropy $$= \dfrac{Energy}{temp} = \dfrac{M^{1} L^{2} T^{-2}}{K} = M^{1} L^{2} T^{-2} K^{-1}$$

Latent heat $$= \dfrac{Energy}{Mass} = \dfrac{M^{1} L^{2} T^{-2}}{M^{1}} = L^{2} T^{-2}$$

Heat $$= M^{1} L^{2} T^{-2}$$

Specific heat $$= \dfrac{Energy}{M\times T} = \dfrac{M^{1} L^{2} T^{-2}}{M^{1} K^{1}} = L^{2} T^{-2} K^{-1}$$

Thermal capacity $$= \dfrac{Energy}{temp} = \dfrac{M^{1} L^{2} T^{-2}}{K^{1}} = M^{1} L^{2} T^{-2} K^{-1}$$
Question 9
1 / -0

The dimensional equation for magnetic flux is:

A
$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ -1 }$$

B
$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ -2 }$$

C
$${ ML }^{ -2 }{ T }^{ -2 }{ I }^{ -1 }$$

D
$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ 2 }$$

Solution

Magnetic flux $$=$$ Magnetic Field (B) x Area (A)
B's dimensions $$=$$ Tesla $$= MI^{-1}T^{-2}$$
A's dimensions $$= L^2$$
Therefore, $$BA= ML^2T^{-2}I^{-1}$$
Question 10
1 / -0

"Impulse per unit area" has same dimensions as that of

A
coefficient of viscosity

B
surface tension

C
bulk modulus

D
gravitational potential

Solution

Impulse per unit area $$\displaystyle = \frac{f\times t}{L^{2}} = \frac{M^{1} L^{1} T^{-2}\times T^{1}}{L^{2}} =M^{1} L^{-1} T^{-1}$$

Coeff. of viscosity $$= M^{1} L^{-1} T^{-1}$$

Surface Tension $$= \dfrac{f}{l} = \dfrac{M^{1} L^{1} T^{-2}}{L} = MT^{-2}$$

Bulk Modulus $$= \dfrac{dp}{\dfrac{dv}{v}} = M^{1} L^{-1} T^{-2}$$

Gravitational poential $$\displaystyle = \frac{GM}{r} = \frac{foru\times r}{Mass} = \frac{M^{1} L^{1} T^{-2}\times L^{1}}{M^{1}} = L^{2} T^{-2}$$

Hence, option A is correct.

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Units and Measurements Test - 20

Result

Units and Measurements Test - 20

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SHARING IS CARING

Question 1

$$[{ M }^{ 1 }{ L }^{ 2 }{ T }^{ -1 }]$$

$$[{ M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 }]$$

$$[{ M }^{ -1 }{ L }^{ 2 }{ T }^{ -2 }]$$

$$[{ M }^{ 1 }{ L }^{ 1 }{ T }^{ -2 }]$$

Solution

Question 2

absolute error

relative error

percentage error

Both B and C

Solution

Question 3

mass

length

area

work

Solution

Question 4

$${ M }^{ 0 }{ L }^{ 0 }{ T }^{ 0 }{ A }^{ 0 }$$

$${ M }^{ 2 }{ L }^{ 2 }{ T }^{ 4 }{ A }^{ 2 }$$

$${ M }^{ 2 }{ L }^{ 4 }{ T }^{ -6 }{ A }^{ -4 }$$

$${ M }^{ -2 }{ L }^{ -4 }{ T }^{ 6 }{ A }^{ 4 }$$

Solution

Question 5

a and b

c and b

c and d

d and a

Solution

Question 6

mass

length

time

none

Solution

Question 7

speed of sound

speed of light in vacuum

speed of sound in medium

speed of light in medium

Solution

Question 8

Latent heat

Thermal capacity

Heat

Specific heat

Solution

Question 9

$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ -1 }$$

$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ -2 }$$

$${ ML }^{ -2 }{ T }^{ -2 }{ I }^{ -1 }$$

$${ ML }^{ 2 }{ T }^{ -2 }{ I }^{ 2 }$$

Solution

Question 10

coefficient of viscosity

surface tension

bulk modulus

gravitational potential

Solution

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