Units and Measurements Test

Result

Units and Measurements Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

Dimensions of $$\dfrac { L }{ RCV } $$ are:

A
$${ A }^{ -1 }$$

B
$${ A }^{ -2 }$$

C
$$A$$

D
$${ A }^{ 2 }$$

Solution

Here $$\dfrac{L}{R} = time$$
and $$CV = Q$$
$$\dfrac{t}{Q} = current^{-1}$$
So $$A^{-1}$$ is Correct answer
Question 2
1 / -0

The physical quantity which has the dimensional formula as that of $$\dfrac { energy }{ mass \times length } $$ is:

A
Force

B
Power

C
Pressure

D
Acceleration

Solution

$$\dfrac{energy}{mass\times length}=\dfrac{ML^{2}T^{-2}}{M\times L}=LT^{-2}$$
$$\downarrow $$
(acceleration)
Force$$=MLT^{-2}$$
Power$$=ML^{2}T^{-3}$$
Pressure$$=ML^{-1}T^{-2}$$
Question 3
1 / -0

The length, breadth and thickness of a rectangular lamina are $$1.024\ m$$, $$0.56\ m$$, and $$0.0031\ m$$. The volume, in $${ m }^{ 3 }$$, is:

A
$${ 1.8\times 10 }^{ -3 }$$

B
$${ 1.80\times 10 }^{ -3 }$$

C
$${ 0.180\times 10 }^{ -4 }$$

D
$$0.00177$$

Solution

Volume $$= l\times b\times h=1.777664\times 10^{-3}\ m^3$$
Since, the minimum number of significant figures is $$2$$ (i.e $$0.56$$) out of all quantities, the answer has to be reported in $$2$$ significant digits.
$$\Rightarrow V = 1.8\times 10^{-3} m^{3}$$
Question 4
1 / -0

If $$m$$ is the mass, $$Q$$ is the charge and $$B$$ is the magnetic induction, $$\dfrac{m}{BQ}$$ has the same dimensions as :

A
Frequency

B
Time

C
Velocity

D
Acceleration

Solution

$$F=BQV$$
$$F=ma$$
$$ma=BQV$$

$$\dfrac{m}{BQ}=\dfrac{V}{a}=\dfrac{LT^{-1}}{LT^{-2}}=T$$
Question 5
1 / -0

If the unit of mass is $$\dfrac { 1 }{ 2 } kg$$ and that of length is $$2$$ m and the unit of time is one second, the unit of pressure is:

A
2 pascal

B
0.5 pascal

C
0.25 pascal

D
1.0 pascal

Solution

$$\displaystyle Pressure=\frac{force}{Area}$$
$$=\dfrac{M^{1}L^{1}T^{-2}}{L^{2}}$$
$$=ML^{-1}T^{-2}$$
$$\displaystyle =\frac{1}{2}\times\frac{1}{2}\times \frac{1}{(1)^{2}}\frac{kg}{ms^{2}} $$
$$=\dfrac{1}{4}

=0.25 \ pascal$$
Question 6
1 / -0

If $$C$$ denotes the capacity and $$L$$ denotes the inductance, the dimensions of '$$LC$$' are :

A
$${ M }^{ 0 }{ L }^{ 0 }{ T }^{ 2 }$$

B
$${ M }^{ 1 }{ L }^{ 0 }{ T }^{ 2 }$$

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

D
$${ M }^{ 0 }{ L }^{ 1 }{ T }^{ 2 }$$

Solution

$$L=ML^{2}I^{-2}T^{-2}$$
$$C=M^{-1}L^{-2}I^{2}T^{4}$$
$$LC=M^{0}L^{0}I^{0}T^{2}$$
Question 7
1 / -0

If the fundamental units of length, mass and time are halved, the unit of momentum will be:

A
doubled

B
halved

C
same

D
four times

Solution

$$Momentum=m\times v=MLT^{-1}$$
$$\displaystyle M^{1}=\frac{M}{2}, \ L^{1}=\frac{1}{2}, \ T^{1}=\frac{T}{2}$$
$$\Rightarrow \displaystyle

\frac{\frac{M}{2}\times \frac{L}{2}}{\frac{T}{2}}=\frac{MLT^{-1}}{2}$$
$$\displaystyle \Rightarrow \frac{MLT^{-1}}{2}=\frac{momentum}{2}$$

Hence, option B is correct.
Question 8
1 / -0

The dimensional formula for strain is same as that of

A
thrust

B
angle

C
modulus of elasticity

D
stress

Solution

Strain is the ratio of deformed length to the original, hence is dimensionless. So is the angle.
Option B.
Question 9
1 / -0

The dimensions of the coefficient of viscosity are :

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

B
$$ MLT $$

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

D
$$ M^0L^0T^0 $$
Question 10
1 / -0

The division of energy by time is $$X$$. The dimensional formula of $$X$$ is same as that of

A
momentum

B
power

C
torque

D
electric field

Solution

Energy per unit time is Power. Hence the dimensions would be of the Power.

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Units and Measurements Test - 26

Result

Units and Measurements Test - 26

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SHARING IS CARING

Question 1

$${ A }^{ -1 }$$

$${ A }^{ -2 }$$

$$A$$

$${ A }^{ 2 }$$

Solution

Question 2

Force

Power

Pressure

Acceleration

Solution

Question 3

$${ 1.8\times 10 }^{ -3 }$$

$${ 1.80\times 10 }^{ -3 }$$

$${ 0.180\times 10 }^{ -4 }$$

$$0.00177$$

Solution

Question 4

Frequency

Time

Velocity

Acceleration

Solution

Question 5

2 pascal

0.5 pascal

0.25 pascal

1.0 pascal

Solution

Question 6

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

$${ M }^{ 1 }{ L }^{ 0 }{ T }^{ 2 }$$

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

$${ M }^{ 0 }{ L }^{ 1 }{ T }^{ 2 }$$

Solution

Question 7

doubled

halved

same

four times

Solution

Question 8

thrust

angle

modulus of elasticity

stress

Solution

Question 9

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

$$ MLT $$

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

$$ M^0L^0T^0 $$

Question 10

momentum

power

torque

electric field

Solution

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