Units and Measurements Test

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Units and Measurements Test - 82

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Weekly Quiz Competition

Question 1
1 / -0

In the following list, the only pair which have different dimensions,is

A
Linear momentum and moment of a force

B
Planck's constant and angular momentum

C
Pressure and modulus of elasticity

D
Torque and potential energy

Solution

Linear momentum is given as:
p=$$Mas \times Velocity =[MLT^{-1}]$$

Moment of a force is given as:
Moment =$$ Force\times Distance=[ML^2T^{-2}]$$
Question 2
1 / -0

The dimensions of inter atomic force constant are

A
$$MT^{-2}$$

B
$$MLT^{-1}$$

C
$$MLT^{-2}$$

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

Solution

We know that inter atomic force is given as:
$$K=Y \times r_0=[ML^{-1}T^{-2}]\times [L]=[MT^{-2}]$$
Y = Young's modulus and $$r_0$$ = Interatomic distance
Question 3
1 / -0

If R and L represent respectively resistance and self inductance,which of the following combinations has the dimensions of frequency

A
$$\dfrac{R}{L}$$

B
$$\dfrac{L}{R}$$

C
$$\sqrt{\dfrac{R}{L}}$$

D
$$\sqrt{\dfrac{l}{R}}$$

Solution

We know that ohm law is represented as:
$$V=IR\Rightarrow R=\dfrac VI$$

Whereas Inductance $$L$$ is given as:
$$L=V\times\dfrac TI$$

So, the ratio is given as:
$$\dfrac{R}{L}=\dfrac{V/I}{V \times T /I}=\dfrac{1}{T}$$=Frequency.
Question 4
1 / -0

The dimensions of surface tension are

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

B
$$MLT^{-2}$$

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

D
$$MT^{-2}$$

Solution

The surface tension is given as:
Surface tension =$$\dfrac{Force}{Length}$$

$$=\dfrac{[MLT^{-2}]}{L}=[MT^{-2}]$$
Question 5
1 / -0

The dimensions of $$CV^2$$ matches with the dimensions of

A
$$L^2 I$$

B
$$L^2 I^2$$

C
$$L I^2$$

D
$$\dfrac{1}{LI}$$

Solution

The energy of the capacitor is given by $$E=\dfrac 12 CV^2$$

So, $$CV^2$$ has the dimension of energy. Similarly, $$\dfrac12 Li^2$$ also has the dimension of energy.

So, Both are the formula of energy.$$(E=\dfrac{1}{2}CV^2=\dfrac{1}{2}LI^2)$$

Thus, $$Li^2$$ and $$CV^2$$ have the same dimensions.
Question 6
1 / -0

The pair having the same dimensions is

A
Angular momentum, work

B
Work, torque

C
Potential energy, linear momentum

D
Kinetic energy, velocity

Solution

The work done is defined as the product of work done and displacement.
$$Work = Force\times displacement$$

The torque is also defined as the product of force and perpendicular distance.
$$\tau=Force\times perpendicular\ distance$$

So, Dimension of work and torque =$$[ML^2T^{-2}]$$
Question 7
1 / -0

Which physical quantities have the same dimension

A
Couple of force and work

B
Force and power

C
Latent heat and specific heat

D
Work and power

Solution

Couple of force =$$|\underset{r}{\rightarrow} \times \underset{F}{\rightarrow}|=[ML^2T^{-2}]$$

Work=$$[\underset{r}{\rightarrow}. \underset{F}{\rightarrow}]=[ML^2T^{-2}]$$

So, option $$A$$ is correct
Question 8
1 / -0

The dimensional formula for young's modulus is

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

B
$$M^0LT^{-2}$$

C
$$MLT^{-2}$$

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

Solution
Question 9
1 / -0

Which of the following quantities is dimensionless

A
Gravitational constant

B
Planck's constant

C
Power of a convex lens

D
None

Solution
Question 10
1 / -0

The dimensions of pressure is equal to

A
Force per unit volume

B
Energy per unit volume

C
Force

D
Energy

Solution

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Units and Measurements Test - 82

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Units and Measurements Test - 82

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Question 1

Linear momentum and moment of a force

Planck's constant and angular momentum

Pressure and modulus of elasticity

Torque and potential energy

Solution

Question 2

$$MT^{-2}$$

$$MLT^{-1}$$

$$MLT^{-2}$$

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

Solution

Question 3

$$\dfrac{R}{L}$$

$$\dfrac{L}{R}$$

$$\sqrt{\dfrac{R}{L}}$$

$$\sqrt{\dfrac{l}{R}}$$

Solution

Question 4

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

$$MLT^{-2}$$

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

$$MT^{-2}$$

Solution

Question 5

$$L^2 I$$

$$L^2 I^2$$

$$L I^2$$

$$\dfrac{1}{LI}$$

Solution

Question 6

Angular momentum, work

Work, torque

Potential energy, linear momentum

Kinetic energy, velocity

Solution

Question 7

Couple of force and work

Force and power

Latent heat and specific heat

Work and power

Solution

Question 8

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

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

$$MLT^{-2}$$

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

Solution

Question 9

Gravitational constant

Planck's constant

Power of a convex lens

None

Solution

Question 10

Force per unit volume

Energy per unit volume

Force

Energy

Solution

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