Units and Measurements Test

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Units and Measurements Test - 53

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Weekly Quiz Competition

Question 1
1 / -0

Instrument used to measure the temperature is

A
protractor

B
stethoscope

C
thermometer

D
none of these

Solution

A thermometer is a device that measures the temperature of a body.
Question 2
1 / -0

What is the dimensional formula of gravitational constant?

A
$$\left [ML^{2} T^{-2}\right ]$$

B
$$\left [ML^{-1} T^{-1}\right ]$$

C
$$\left [M^{-1}L^{3} T^{-2}\right ]$$

D
none of these

Solution

$$F = \dfrac {G.M.M}{L^{2}} = MLT^{-2}$$

$$G = \dfrac {MLT^{-2} L^{2}}{M^{2}} = M^{-1} L^{3} T^{-2}$$
Question 3
1 / -0

The dimensional formula of magnetic flux is

A
$$\left [ML^{0} T^{-2} A^{-1}\right ]$$

B
$$\left [ML^{2} T^{-2} A^{-1}\right ]$$

C
$$\left [ML^{2} T^{-1} A^{3}\right ]$$

D
$$\left [M^{0}L^{-2} T^{-2} A^{-2}\right ]$$

Solution

$$F = Bqv \rightarrow F = \dfrac {\phi}{A} qv$$

$$\phi = \dfrac {F . A}{qv} = \dfrac {MLT^{-2} L^{2}}{ATLT^{-1}} = ML^{+2} A^{-1} T^{-2}$$
Question 4
1 / -0

Write the dimensional formula of Force.

A
$$MLT$$

B
$$MLT^{-2}$$

C
$$MLT^2$$

D
None of the above

Solution

Force $$=$$ mass $$\times $$ acceleration
$$[F]=[M]\times [LT^{-2}]=MLT^{-2}$$
Question 5
1 / -0

Dimensions of electrical resistance are

A
$$\left [ML^{2} T^{-3} A^{-1}\right ]$$

B
$$\left [ML^{2} T^{-3} A^{-2}\right ]$$

C
$$\left [ML^{3} T^{-3} A^{-2}\right ]$$

D
$$\left [ML^{-1} L^{3} T^{3} A^{2}\right ]$$

Solution
Question 6
1 / -0

Using mass ($$M$$), length ($$L$$), time ($$T$$) and current ($$A$$) as fundamental quantities, the dimensional formula of permittivity is

A
$$\left [ML^{-2}T^{2} A\right ]$$

B
$$\left [M^{-1} L^{-3}T^{4} A^{2}\right ]$$

C
$$\left [MLT^{-2} A\right ]$$

D
$$\left [ML^{2}T^{-1} A^{2}\right ]$$

Solution

$$F = \dfrac {1}{4\pi \epsilon_{0}} \cdot \dfrac {q_{1} q_{2}}{r^{2}} \Rightarrow \epsilon_{0} = \dfrac {q_{1}q_{2}}{4\pi Fr^{2}}$$

$$\dfrac {AT \cdot AT}{MLT^{-2} L^{2}} = \dfrac {A^{2}T^{2}}{ML^{3} T^{-2}} = M^{-1} L^{-3} A^{2} T^{4}$$
Question 7
1 / -0

The dimensions of torque are

A
$$\left [ML^{3}T^{-3}\right ]$$

B
$$\left [ML^{-1}T^{-1}\right ]$$

C
$$\left [ML^{2}T^{-2}\right ]$$

D
$$\left [MT^{-2}\right ]$$

Solution
Question 8
1 / -0

Using mass $$(M)$$, length $$(L)$$, time $$(T)$$ and current $$(A) $$as fundamental quantities, the dimensions of permeability are

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

B
$$\left [M^{-2} L T^{-2} A^{-1}\right ]$$

C
$$\left [MLT^{-2} A^{-2}\right ]$$

D
$$\left [MLT^{-1} A^{-1}\right ]$$

Solution

$$B = \mu ni; F = Bqv$$

$$F = \mu ni qv \Rightarrow \mu = \dfrac {F}{niqv}$$

$$\mu = \dfrac {MLT^{-2}}{\dfrac {1}{L} A.AT.LT^{-1}}$$ [n is no. of turns per unit length]

$$= MLA^{-2} T^{-2}$$
Question 9
1 / -0

The relation between force $$F$$ and density $$d$$ is $$F = \dfrac{x}{\sqrt{d}}$$. The dimensions of $$x$$ are

A
$$\left[{L}^{{-1}/{2}}{M}^{{3}/{2}}{T}^{-2}\right]$$

B
$$\left[{L}^{{-1}/{2}}{M}^{{1}/{2}}{T}^{-2}\right]$$

C
$$\left[{L}^{-1}{M}^{{3}/{2}}{T}^{-2}\right]$$

D
$$\left[{L}^{-1}{M}^{{1}/{2}}{T}^{-2}\right]$$

Solution

Given, $$F = \dfrac{x}{\sqrt{d}}$$
Substituting dimensions
$$ML{T}^{-2} = \dfrac{x}{\sqrt{M{L}^{-3}}}$$
$$\Rightarrow x = \left[{M}^{{3}/{2}}{L}^{{-1}/{2}}{T}^{-2}\right]$$
Question 10
1 / -0

The dimensional formula for torque is

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

B
$$ML^{-1} T^{-1}$$

C
$$L^{2} T^{-1}$$

D
$$M^{2} T^{-2} K^{-1}$$

Solution

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Units and Measurements Test - 53

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Units and Measurements Test - 53

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SHARING IS CARING

Question 1

protractor

stethoscope

thermometer

none of these

Solution

Question 2

$$\left [ML^{2} T^{-2}\right ]$$

$$\left [ML^{-1} T^{-1}\right ]$$

$$\left [M^{-1}L^{3} T^{-2}\right ]$$

none of these

Solution

Question 3

$$\left [ML^{0} T^{-2} A^{-1}\right ]$$

$$\left [ML^{2} T^{-2} A^{-1}\right ]$$

$$\left [ML^{2} T^{-1} A^{3}\right ]$$

$$\left [M^{0}L^{-2} T^{-2} A^{-2}\right ]$$

Solution

Question 4

$$MLT$$

$$MLT^{-2}$$

$$MLT^2$$

None of the above

Solution

Question 5

$$\left [ML^{2} T^{-3} A^{-1}\right ]$$

$$\left [ML^{2} T^{-3} A^{-2}\right ]$$

$$\left [ML^{3} T^{-3} A^{-2}\right ]$$

$$\left [ML^{-1} L^{3} T^{3} A^{2}\right ]$$

Solution

Question 6

$$\left [ML^{-2}T^{2} A\right ]$$

$$\left [M^{-1} L^{-3}T^{4} A^{2}\right ]$$

$$\left [MLT^{-2} A\right ]$$

$$\left [ML^{2}T^{-1} A^{2}\right ]$$

Solution

Question 7

$$\left [ML^{3}T^{-3}\right ]$$

$$\left [ML^{-1}T^{-1}\right ]$$

$$\left [ML^{2}T^{-2}\right ]$$

$$\left [MT^{-2}\right ]$$

Solution

Question 8

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

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

$$\left [MLT^{-2} A^{-2}\right ]$$

$$\left [MLT^{-1} A^{-1}\right ]$$

Solution

Question 9

$$\left[{L}^{{-1}/{2}}{M}^{{3}/{2}}{T}^{-2}\right]$$

$$\left[{L}^{{-1}/{2}}{M}^{{1}/{2}}{T}^{-2}\right]$$

$$\left[{L}^{-1}{M}^{{3}/{2}}{T}^{-2}\right]$$

$$\left[{L}^{-1}{M}^{{1}/{2}}{T}^{-2}\right]$$

Solution

Question 10

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

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

$$L^{2} T^{-1}$$

$$M^{2} T^{-2} K^{-1}$$

Solution

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