Units and Measurements Test

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Units and Measurements Test - 31

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Weekly Quiz Competition

Question 1
1 / -0

The dimensional formula of velocity gradient is

A
$$[M^0L^0T^{-1}]$$

B
$$[MLT^{-1}]$$

C
$$[ML^0T^{-1}]$$

D
$$[M^0LT^{-2}]$$

Solution

Velocity Gradient $$V$$ is defined as rate of change in velocity per unit of distance. Mathematically, Velocity Gradient= velocity/distance.
Dimensionally $$V=\dfrac { \left[ { M }^{ 0 }{ L }^{ 1 }{ T }^{ -1 } \right] }{ \left[ L \right] } =\left[ { M }^{ 0 }{ L }^{ 0 }{ T }^{ -1 } \right] $$
Question 2
1 / -0

Which of the following is the unit of molar gas constant?

A
$$JK^{-1} mol^{-1}$$

B
$$J$$

C
$$JK^{-1}$$

D
$$Jmol^{-1}$$

Solution

Molar gas constant is given as $$R=\dfrac {PV}{nT}$$
So, unit of $$R=\dfrac {Joule}{mol K}=JK^{-1} mol^{-1}$$
Question 3
1 / -0

Dimensions of '$$ohm$$' are same as (where $$h$$ is Planck's constant and $$e$$ is charge)

A
$$\dfrac {h}{e}$$

B
$$\dfrac {h^2}{e}$$

C
$$\dfrac {h}{e^2}$$

D
$$\dfrac {h^2}{e^2}$$

Solution

'ohm' is the unit of resistance and having dimension $$ =[ML^2T^{-3}A^{-2}]$$
From option C $$\Rightarrow \dfrac {h}{e^2}=\dfrac {ML^2T{-1}}{(AT)^2}=[ML^2T^{-3}A^{-2}]=Resistance (ohm)$$
Question 4
1 / -0

If $$C$$ and $$L$$ denote the capacitance and inductance, the dimensions of $$LC$$ are

A
$$[M^0L^0T^{-1}]$$

B
$$[M^0L^{-1}T^0]$$

C
$$[M^{-1}L^{-1}T^0]$$

D
$$[M^0L^0T^{2}]$$

Solution

The frequency $$v$$ of a circuit consisting of capacitance and inductance is given as $$v=\dfrac {1}{2\pi \sqrt {LC}}$$
So, $$[LC]=\dfrac {1}{(2\pi v)^2}=\dfrac {1}{(T^{-1})^2}=[T^2]=[M^0L^0T^2]$$
Question 5
1 / -0

If $$I$$ is regarded as the fourth dimension, then the dimensional formula of charge in terms of current $$I$$ is

A
$$[IT^2]$$

B
$$[I^0T^0]$$

C
$$[I^{-1}T^0]$$

D
$$[IT]$$

Solution

An electric current is defined as a rate of flow of electric charge q.
So, $$I=\dfrac {q}{t}$$ or $$[q]=[IT]$$
Question 6
1 / -0

Specific gravity has ___ dimensions in mass, ___ dimensions in length and ___ dimensions in time.

A
0, 0, 0

B
0, 1, 0

C
1, 0, 0

D
1, 1, 3

Solution

Specific gravity is the ratio of density of substance and density of water at $$ { 4 }^{ o }C$$. Hence it is the ratio of like quantities, therefore dimensionless.
Question 7
1 / -0

The dimensions of torque are

A
$$[MLT^{-2}]$$

B
$$[ML^2T^{-2}]$$

C
$$[ML^2T^{-1}]$$

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

Solution
Question 8
1 / -0

How many order of magnitude are there in one million?

A
5

B
4

C
6

D
None of above

Solution

For the number 1,000,000, we will shift the decimal to the left, stopping just before the first digit of the number. The number of moves you make to the left is the order of magnitude. Since we moved it six times, there are six orders of magnitude of 1,000,000, meaning that you can multiply 10 six times and get 1,000,000
Question 9
1 / -0

Dimensional formula of power is

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

B
$$[ML^2T^{-3}]$$

C
$$[M^2LT^{-2}]$$

D
$$[MLT^{-2}]$$

Solution

$$Power = force \times velocity$$
$$P = F \times v$$
$$F=\left[ ML{ T }^{ -2 } \right] $$
$$v=\left[ L{ T }^{ -1 } \right] $$
Therefpre, the dimensional formula of power, $$P = \left[ ML{ T }^{ -2 } \right] \times \left[ L{ T }^{ -1 } \right] = \left[ M{ L }^{ 2 }{ T }^{ -3 } \right] $$
Question 10
1 / -0

The thickness of a metal sheet is measured to be $$326 mm$$. Express its order of magnitude in mm.

A
$$10^0$$

B
$$10^1$$

C
$$10^2$$

D
$$10^3$$

Solution

Thickness $$t = 326\ mm$$
$$= 3.26 \times 10^2\ mm$$
Hence, order of magnitude in mm is $$10^2$$.

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Units and Measurements Test - 31

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Units and Measurements Test - 31

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Question 1

$$[M^0L^0T^{-1}]$$

$$[MLT^{-1}]$$

$$[ML^0T^{-1}]$$

$$[M^0LT^{-2}]$$

Solution

Question 2

$$JK^{-1} mol^{-1}$$

$$J$$

$$JK^{-1}$$

$$Jmol^{-1}$$

Solution

Question 3

$$\dfrac {h}{e}$$

$$\dfrac {h^2}{e}$$

$$\dfrac {h}{e^2}$$

$$\dfrac {h^2}{e^2}$$

Solution

Question 4

$$[M^0L^0T^{-1}]$$

$$[M^0L^{-1}T^0]$$

$$[M^{-1}L^{-1}T^0]$$

$$[M^0L^0T^{2}]$$

Solution

Question 5

$$[IT^2]$$

$$[I^0T^0]$$

$$[I^{-1}T^0]$$

$$[IT]$$

Solution

Question 6

0, 0, 0

0, 1, 0

1, 0, 0

1, 1, 3

Solution

Question 7

$$[MLT^{-2}]$$

$$[ML^2T^{-2}]$$

$$[ML^2T^{-1}]$$

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

Solution

Question 8

5

4

6

None of above

Solution

Question 9

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

$$[ML^2T^{-3}]$$

$$[M^2LT^{-2}]$$

$$[MLT^{-2}]$$

Solution

Question 10

$$10^0$$

$$10^1$$

$$10^2$$

$$10^3$$

Solution

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