Units and Measurements Test

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Units and Measurements Test - 79

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Weekly Quiz Competition

Question 1
1 / -0

The Earth's radius is $$6371\ km$$. The order of magnitude of the Earth's radius is

A
$$10^3$$

B
$$10^2$$

C
$$10^7$$

D
$$10^5$$

Solution

Order of magnitude is usually written as $$10 $$ to the $$n$$th power. The represents the order of magnitude.
e.g., if we write a number $$X$$ in such a way that
$$X = m × 10^n$$ then n is order of magnitude.
Where $$ \dfrac{\sqrt{10}}{10} \leq m \leq \sqrt{10}$$
here, $$6371 km = 6371000 m$$
$$6371000 = 6.371 × 10^6$$
we see, $$ 6.371 ≥ \sqrt{10}$$
so, $$0.6371 × 10^7$$
now, $$ \dfrac{\sqrt{10}}{10} \leq 0.6371 \leq \sqrt{10}$$
$$ \therefore 7$$ is our order of magnitude.
Question 2
1 / -0

The diagram shows a cuboid block made from a metal of density $$2.5g/{cm}^{3}$$
What is the mass of the block?

A
$$8.0kg$$

B
$$16kg$$

C
$$50g$$

D
$$100g$$

Solution

Volume of cuboid = $$l \times b \times h$$
                             = $$10 \times 2 \times 2$$ $$cm^{3}$$
                              = $$40 cm^3$$
Now , Mass = $$V \times d$$
                     = $$40 \times 2.5$$ $$g$$
                      = $$100g$$
Question 3
1 / -0

In the density measurement of a cube, the mass an edge length are measured as $$\left( 10.00\pm 0.10 \right) kg$$ and $$\left( 0.10\pm 0.01 \right) m$$, respectively. The error in the measurement of density:

A
$$0.10kg/{m}^{3}$$

B
$$0.31kg/{m}^{3}$$

C
$$0.07kg/{m}^{3}$$

D
$$0.01kg/{m}^{3}$$

E
No answer

Solution

$$\rho =\cfrac { m }{ v } $$
$$\cfrac { \Delta \rho }{ \rho } \times 100percent=\cfrac { \Delta m }{ m } \times 100percent+3\left( \cfrac { \Delta L }{ L } \right) \times 100percent....(i)$$
which is only possible when error is small which is not the case in this question
Yet if we apply equation (i) we get
$$\Delta \rho =3100kg/{ m }^{ 3 }\quad $$
Now we will calculate error, without using approximation
$${ \rho }_{ min }=\cfrac { { m }_{ min } }{ { v }_{ max } } =\cfrac { 9.9 }{ { \left( 0.11 \right) }^{ 3 } } =7438kg/{ m }^{ 3 }$$
and $$\quad { \rho }_{ max }=\cfrac { { m }_{ max } }{ { v }_{ min } } =\cfrac { 10.1 }{ { \left( 0.09 \right) }^{ 3 } } =13854kg/{ m }^{ 3 }$$
$$\Delta \rho =6416.6kg/{ m }^{ 3 }$$
No option is matching
Question 4
1 / -0

The dimension of Magnetic flux.

A
$$ML^{2}I^{-1}T^{-3}$$

B
$$ML^{2}I^{-4}T^{-2}$$

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

D
None of these
Question 5
1 / -0

The dimension of $$ \frac {1}{2} \varepsilon _ o E^2 ( \varepsilon _ o $$ is the permitivity of free space and E is electric field) is

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

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

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

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

Solution
Question 6
1 / -0

If x,v and a denote the displacement, the velocity and the acceleration of a particle
executing simple harmonic motion of time period T, then which of the following do not
change with time?

A
$$\dfrac{aT}{v}$$

B
$$aT+2\pi v$$

C
$$a^2T^2+4\pi^2 v^2$$

D
$$aT$$

E
$$vT$$

Solution

$$\because$$ In option $$(a),\dfrac{aT}{v}=\dfrac{\dfrac{m}{s^2}\times s}{\left(\dfrac{m}{s}\right)}=\dfrac{m\times s^2}{m\times s^2}=[M^0L^0T^0]$$
So, according to the result above relation does not depend on time
Question 7
1 / -0

Which of the following does not have the dimension of force?

A
Potential gradient

B
Energy gradient

C
Weight

D
Rate of change of momentum

Solution
Question 8
1 / -0

The mass of a neutral carbon atom in ground state is

A
exact $$12\,u$$

B
less than $$12\,u$$

C
more than $$12\,u$$

D
depends on the form of carbon such as graphite a=or charcoal

Solution
Question 9
1 / -0

If $$P$$ and $$Q$$ have different non-zero dimensions, which of the following operations is possible?

A
$$P+Q$$

B
$$PQ$$

C
$$P-Q$$

D
$$ 1-\dfrac{P}{Q} $$

Solution
Question 10
1 / -0

Which of the following sets have different dimensions?

A
Pressure, Young's modulus, stress

B
Emf, potential difference, electric potential

C
Heat, work done, energy

D
Dipole moment, electric flux, electric field

Solution

Dipole moment is the coulomb–meter.
Electric flux is the rate of flow of the electric field through a given area.
Electric field is volt per meter (V/m).

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Re-Attempt Weekly Quiz Competition

Units and Measurements Test - 79

Result

Units and Measurements Test - 79

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SHARING IS CARING

Question 1

$$10^3$$

$$10^2$$

$$10^7$$

$$10^5$$

Solution

Question 2

$$8.0kg$$

$$16kg$$

$$50g$$

$$100g$$

Solution

Question 3

$$0.10kg/{m}^{3}$$

$$0.31kg/{m}^{3}$$

$$0.07kg/{m}^{3}$$

$$0.01kg/{m}^{3}$$

No answer

Solution

Question 4

$$ML^{2}I^{-1}T^{-3}$$

$$ML^{2}I^{-4}T^{-2}$$

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

None of these

Question 5

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

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

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

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

Solution

Question 6

$$\dfrac{aT}{v}$$

$$aT+2\pi v$$

$$a^2T^2+4\pi^2 v^2$$

$$aT$$

$$vT$$

Solution

Question 7

Potential gradient

Energy gradient

Weight

Rate of change of momentum

Solution

Question 8

exact $$12\,u$$

less than $$12\,u$$

more than $$12\,u$$

depends on the form of carbon such as graphite a=or charcoal

Solution

Question 9

$$P+Q$$

$$PQ$$

$$P-Q$$

$$ 1-\dfrac{P}{Q} $$

Solution

Question 10

Pressure, Young's modulus, stress

Emf, potential difference, electric potential

Heat, work done, energy

Dipole moment, electric flux, electric field

Solution

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