Units and Measurements Test

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Units and Measurements Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

A pair of physical qunatities having the same dimensional formula are:

A
momentum and impulse

B
momentum and energy

C
energy and pressure

D
force and power

Solution

Momentum $$\rightarrow mv=M^{1}L^{1}T^{-1}$$
Impulse $$\rightarrow f\times t=M^{1}L^{1}T^{-1}$$
Energy $$=ML^{2}T^{-2}$$
Pressure $$=ML^{-1}T^{-2}$$
Power $$=ML^{2}T^{-3}$$
Hence, option A is correct.
Question 2
1 / -0

Modulus of Elasticity is dimensionally equivalent to:

A
Stress

B
Surface tension

C
Strain

D
Coefficient of viscosity

Solution

Modulus of elasticity $$=M^{1}L^{-1}T^{-2}$$
Stress $$=M^{1}L^{-1}T^{-2}$$
Surface tension $$=\dfrac{f}{l}=M^{1}L^{0}T^{-2}$$
Strain $$=\dfrac{\Delta L}{L}=M^{0}L^{0}T^{0}$$
Coeff of viscosity$$=F/A\dfrac{dv_{x}}{dx}=\dfrac{MLT^{-2}}{L^{2}\dfrac{LT^{-1}}{L}}=ML^{-1}T^{-1}$$
Hence, option A is correct.
Question 3
1 / -0

A pair of physical quantities having the same dimensional formula are:

A
Force and Work

B
Work and Energy

C
Force and Torque

D
Work and Power

Solution

Force$$=M^{1}L^{1}T^{-2}$$
Work$$=ML^{2}T^{-2}$$
Energy$$=ML^{2}T^{-2}$$
Torque$$=ML^{2}T^{-2}$$
Power$$=ML^{3}T^{-3}$$
Hence, option B is correct.
Question 4
1 / -0

The physical quantities not having same dimensions are :

A
torque and work

B
momentum and Plancks constant

C
stress and Youngs modulus

D
speed and $$\left( { \mu }_{ 0 }{ \epsilon }_{ 0 } \right) ^{ -1/2 }$$

Solution

$$\dfrac{1}{\sqrt{\mu _{0}\epsilon _{0}}}=\sqrt{L^{2}T^{-2}}=LT^{-1}$$
Speed $$=LT^{-1}$$
Stress, Young's modulus $$=\dfrac{MLT^{-2}}{L^{2}}=ML^{-1}T^{-2}$$
Momentum $$=MLT^{-1}$$
Torque, Work $$=ML^{2}T^{-2}$$
Planck's constant $$=\dfrac{ML^{2}T^{-2}}{\left ( LT^{-1} \right )}\times L=ML^{2}T^{-1}$$
Hence, option B is correct.
Question 5
1 / -0

The dimensional formula for universal gravitational constant is:

A
$${ M }^{ 1 }{ L }^{ 3 }{ T }^{ -2 }$$

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

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

D
$${ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 }$$

Solution

The correct option is $$D.$$

Formula for Gravitational force is:

$$F= \dfrac{G M m}{r^{2}}$$

So, Formula for G will be,

$$G = \dfrac{F r^{2}}{M m}$$

Thus, the dimensional formula for G is,

$$M^{-1}L^{3}T^{-2}$$
Question 6
1 / -0

Which one of the following represents the correct dimensions of the coefficient of viscosity ?

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

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

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

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

Solution

For calculating coefficient of viscosity we can use the formula, $$F=\dfrac{\eta vA}{S}$$
Dimension of coefficient of viscosity will be $$=\dfrac{Dimension \ of \ force \times Distance}{Velocity \times Area}$$

$$=\dfrac{MLT^{-2}\times L}{LT^{-1}L^2}$$

$$=ML^{-1}T^{-1}$$
Question 7
1 / -0

The pair of physical quantities having the same dimensional formula is:

A
angular momentum and torque

B
torque and strain energy

C
entropy and power

D
power and angular momentum

Solution

Angular momentum $$=M^{1}L^{2}T^{-1}$$
Torque $$=ML^{2}T^{-2}$$
Strain energy $$=\frac{1}{2} \times ML^{2}T^{-2}$$
Entropy $$=ML^{2}T^{-2}K^{-1}$$
Power $$=ML^{2}T^{-3}$$
Hence torque and strain energy has same dimensions,
Question 8
1 / -0

Dimensional formula of Torque is:

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

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

C
$${ ML }^{ 2 }{ T }^{ -3 }$$

D
$${ MLT }^{ -3 }$$
Question 9
1 / -0

Dimensions of $$\dfrac { 1 }{ { \mu }_{ 0 }{ \epsilon }_{ 0 } } $$ , where symbols have their usual meaning are :

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

B
$${ L }^{ 2 }{ T }^{ 2 }$$

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

D
$${ LT }^{ -1 }T$$
Question 10
1 / -0

Planck's constant has the dimensions as that of:

A
Energy

B
Power

C
Linear momentum

D
Angular momentum

Solution

Plank's constant $$=ML^{2}T^{-1}$$
Energy $$=M^{1}L^{2}T^{-2}$$
Power $$=M^{1}L^{2}T^{-3}$$
Linear momentum $$=MLT^{-1}$$
Angular momentum $$=ML^{2}T^{-1}$$
Hence, option D is correct.

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Units and Measurements Test - 22

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Units and Measurements Test - 22

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Question 1

momentum and impulse

momentum and energy

energy and pressure

force and power

Solution

Question 2

Stress

Surface tension

Strain

Coefficient of viscosity

Solution

Question 3

Force and Work

Work and Energy

Force and Torque

Work and Power

Solution

Question 4

torque and work

momentum and Plancks constant

stress and Youngs modulus

speed and $$\left( { \mu }_{ 0 }{ \epsilon }_{ 0 } \right) ^{ -1/2 }$$

Solution

Question 5

$${ M }^{ 1 }{ L }^{ 3 }{ T }^{ -2 }$$

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

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

$${ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 }$$

Solution

Question 6

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

$${ MLT }^{ -1 }$$

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

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

Solution

Question 7

angular momentum and torque

torque and strain energy

entropy and power

power and angular momentum

Solution

Question 8

$${ MLT }^{ -2 }$$

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

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

$${ MLT }^{ -3 }$$

Question 9

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

$${ L }^{ 2 }{ T }^{ 2 }$$

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

$${ LT }^{ -1 }T$$

Question 10

Energy

Power

Linear momentum

Angular momentum

Solution

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