Units and Measurements Test

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Units and Measurements Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$[L^{-1_{/2}}M^{3_{/2}}T^{-2}]$$

B
$$[L^{-1_{/2}}M^{1_{/2}}T^{-2}]$$

C
$$[L^{-1}M^{3_{/2}}T^{-2}]$$

D
$$[L^{-1}M^{1_{/2}}T^{-2}]$$

Solution

The quantity is $$x = F \sqrt{d}$$
Dimensions of force $$F = [M^1 L^1 T^{-2}]$$
Dimensions of density $$d = [M^1 L^{-3}]$$
Dimensions of $$x$$ are $$[x] = [M^1 L^1 T^{-2}] [M^1 L^{-3}]^{1/2}$$
$$\implies$$ $$[x] = [M^{3/2} L^{-1/2} T^{-2}]$$
Question 2
1 / -0

Which one of the following pair of quantities has same dimension?

A
Force and work done

B
Momentum and impulse

C
Pressure and force

D
Surface tension and stress

Solution

Impulse= Change in momentum
Hence, impulse and momentum both have same dimensions i.e., [MLT−1]
Question 3
1 / -0

Dimensions $$[ML^{-1}T^{-1}]$$ are related to

A
Torque

B
Work

C
Energy

D
Coefficient of viscosity

Solution

We know that
Coefficient of viscosity=$$\displaystyle \frac{force/area}{velocity\,\,gradient}$$
$$\displaystyle [\eta] =\frac{[MLT^{-2}]/[L^2]}{[LT^{-1}]/[L]}$$
$$\displaystyle =[ML^{-1}T^{-1}]$$
Question 4
1 / -0

If acceleration ($$A$$), mass ($$M$$), velocity ($$V$$), time ($$T$$) are the fundamental units, then the dimensions of height will be

A
$$V{ T }^{ -1 }{ M }^{ 2 }\quad $$

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

C
$${ A }^{ -1 }{ M }^{ 3 }{ V }^{ -1 }$$

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

Solution

Given, acceleration $$(A)$$, mass $$(m)$$, velocity $$(v)$$, time $$(T)$$
Hence, $$\quad A=\left[ L{ T }^{ -2 } \right] \quad \Rightarrow \left[ L \right] =\left[ A{ T }^{ 2 } \right] $$
Question 5
1 / -0

The dimension of universal gravitational constant is :

A
$$[M^{-2}L^{-3}T^{-2}]$$

B
$$[M^{-2}L^2T^{-1}]$$

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

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

Solution

$$F=\displaystyle\frac{Gm_1m_2}{r^2}$$
$$\Rightarrow \displaystyle G=\frac{Fr^2}{m_1m_2}=\frac{[MLT^{-2}][L^2]}{[M^2]}$$
$$=\displaystyle [M^{-1}L^3T^{-2}]$$.
Question 6
1 / -0

The pressure on a square plate is measured by measuring the force on the plate. If the maximum error in the measurement of force and length are respectively $$4\%$$ and $$2\%$$, then the maximum error in the measurement of pressure is :

A
$$1\%$$

B
$$2\%$$

C
$$4\%$$

D
$$8\%$$

Solution

As per question,
Error in the measurement of the force$$=4\%$$
Error in the measurement of the length $$=2\%$$
Pressure $$=\dfrac{force}{area}=\dfrac{F}{L^2}$$
$$\therefore \dfrac{\triangle p}{p}=\dfrac{\triangle F}{F}+\dfrac{2\triangle L}{L}=4\% +2(2\%)$$
$$=8\%$$
So the maximum error in the measurement of the pressure is $$=8\%$$
Question 7
1 / -0

The dimension of the universal constant of gravitation $$G$$ is

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

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

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

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

Solution

$$\left[ G \right] =\left[ \cfrac { F{ r }^{ 2 } }{ { m }_{ 1 }{ m }_{ 2 } } \right] =\left[ { M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 } \right] $$
Question 8
1 / -0

Which of the following physical quantities has a unit but no dimensions?

A
Relative velocity

B
Relative density

C
Angle

D
Energy

Solution

Among the given physical quantities angle has a unit but no dimensions. Angie = $$[M^0L^0T^0]$$
The SI unit of angle is radian.
Question 9
1 / -0

Possible errors with screw gauge are

A
Systematic error

B
Backlash error

C
Personal error

D
All these

Solution

Screw gauge being a measuring instrument will have systematic error apart from the zero error
Question 10
1 / -0

The error which follows a particular rule is

A
Personal error

B
Systematic error

C
Random error

D
Gross error

Solution

Personal error follows a particular rule.

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Units and Measurements Test - 38

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Units and Measurements Test - 38

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SHARING IS CARING

Question 1

$$[L^{-1_{/2}}M^{3_{/2}}T^{-2}]$$

$$[L^{-1_{/2}}M^{1_{/2}}T^{-2}]$$

$$[L^{-1}M^{3_{/2}}T^{-2}]$$

$$[L^{-1}M^{1_{/2}}T^{-2}]$$

Solution

Question 2

Force and work done

Momentum and impulse

Pressure and force

Surface tension and stress

Solution

Question 3

Torque

Work

Energy

Coefficient of viscosity

Solution

Question 4

$$V{ T }^{ -1 }{ M }^{ 2 }\quad $$

$$AM{ T }^{ -1 }$$

$${ A }^{ -1 }{ M }^{ 3 }{ V }^{ -1 }$$

$$A{ T }^{ 2 }$$

Solution

Question 5

$$[M^{-2}L^{-3}T^{-2}]$$

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

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

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

Solution

Question 6

$$1\%$$

$$2\%$$

$$4\%$$

$$8\%$$

Solution

Question 7

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

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

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

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

Solution

Question 8

Relative velocity

Relative density

Angle

Energy

Solution

Question 9

Systematic error

Backlash error

Personal error

All these

Solution

Question 10

Personal error

Systematic error

Random error

Gross error

Solution

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