Roshan Bhandari

Computer Engineer, IOE Pulchowk

IOE Entrance Exam

  • 432 seats, Computer based
  • 140 marks, 2 hours, no -ve marking

 

Subject

 

Full

Marks

 

Total No of

Questions

 

1M

 

2M

 

English

22

18

14

4

Chemistry

20

16

12

4

Physics

40

25

10

15

Mathematics

40

25

10

15

Engineering Aptitude

18

16

14

2

Unit, Dimension and Error Analysis

Fundamental Quantity

  • 7 fundamental quantities

Mass

  • Do not depend on other quantities

Length

Time

Temperature

Luminous intensity

Electric Current

Amount of substance

Measurement

Measurement is the process of comparing any amount of physical quantity to standard amount of another physical quantity.

Q1: In Astronomy , there is a unit of distance called A.U. - the astronomical unit. This denotes the distance between [BPKIHS 1997]

a)The sun and Earth 

b)The sun and the planet Mercury

c)The Moon and Earth

d)The two poles of Earth (its diameter)

Correct: a

Unit

157cm

50 Kg

10:20 AM

Q2: The fundamental quantity is

a)Specific gravity

b) angle

c) Temperature

d) density

 7 Fundamental Units

Physical Qty

Units

Symbol

Length

Meter

M

Mass

Kilogram

Kg

Time

Second

S

Temperature

Kelvin

K

Luminosity

Candela

Cd

Electric Current

Ampere

A

Amount of substance

Mole

mol

Correct: c

Q3: Which is a supplementary unit?

a)Radian  

b)Second

c) Micron 

d) lux

Supplementary Units

Physical Qty

Units

Symbol

Plane Angle

Radian

R

Solid Angle

Steradian

Sr

Correct: a

Dimension

•The power on fundamental quantities when a physical quantity is expressed in their terms are called dimensions.

Dimension of Time = T

[MLT^{-2}]
[MLT−2][MLT^{-2}]

Dimension of Force = 

Calculation of Dimension 

[M]
[M][M]

Dimension of Force = 

Mass * Acceleration

\frac{Velocity}{Time}
VelocityTime\frac{Velocity}{Time}
\frac{\frac{distance}{Time}}{Time}
distanceTimeTime\frac{\frac{distance}{Time}}{Time}

=

=

[M]
[M][M]
[LT^{-2}]
[LT−2][LT^{-2}]

*

=

[MLT^{-2}]
[MLT−2][MLT^{-2}]

Calculation of Dimension 

Dimension of Work= 

Force * distance

=

[ML^{2}T^{-2}]
[ML2T−2][ML^{2}T^{-2}]
[MLT^{-2}]
[MLT−2][MLT^{-2}]
[L]
[L][L]

Q4: Dimensional Formula of velocity gradient is

[M^0L^0T]
[M0L0T][M^0L^0T]

a) 

[M^0L^0T^{-1}]
[M0L0T−1][M^0L^0T^{-1}]

c) 

[M^{-1}L^0T^0]
[M−1L0T0][M^{-1}L^0T^0]

b) 

[M^0L^0T^0]
[M0L0T0][M^0L^0T^0]

d) 

Correct: c

Q5: Plank’s constant has the dimension of[MOE 2069]

a) Energy 

c) Frequency

b) Mass

d) Angular Momentum

Correct: d

Angular momentum = r * P = r * mv

E = hf = 

\frac{hc}{\lambda}
hcλ\frac{hc}{\lambda}

so, h = 

{mc}*{\lambda}
mc∗λ{mc}*{\lambda}

= L *r = P

Q6: Newton/coulomb has the same dimension of [IOE]

a) Volt /meter

Correct: a

b) Volt-meter

c) Farad/meter

d) Farad-meter

E = \frac{F}{q} = \frac{dv}{dx}
E=Fq=dvdxE = \frac{F}{q} = \frac{dv}{dx}

Q7:  A unit less physical quantity

a) may have non zero dimension

Correct: c

b) must have non zero dimension

c) never has non zero dimension

d) never exists

A unit less physical quantity is always dimensionless but a dimensionless physical quantity may have unit.

Dimensionless physical quantities having unit:

  • Angular Displacement,
  • solid angle,
  • plane angle,
  •  intensity level, etc

Dimensionless and unit less physical quantity:

  • Strain,
  • Mechanical equivalent of Heat
  • Ratio of specific heat
  • Refractive index
  • Relative Permittivity

Significant Figures

Q8: The number of significant figures in 300 is

a) 1

c) 2

b) 3

d) Not defined

Correct: d

Significant figures are defined only for measurement and is number of digits present in measurement.

Q9: The number of significant figures in 3.00 is

a) 1

c) 2

b) 3

d) Not defined

Correct: c

Zeros to the right of nonzero are significant.

Q10: The number of significant figures in 0.054 is

a) 1

c) 2

b) 3

d) Not defined

Correct: c

Zeros to the left of nonzero are insignificant.

Q11: The number of significant figures in 312.1 + 1.32 is

a) 1

c) 4

b) 3

d) Not defined

Correct: c

  • For addition and subtraction, significant figures is taken after the component having less digit after decimal.
  • For multiplication and division, significant figures is taken after the component having less number of significant figure.

Q12:  The density of a material of a cube is calculated by measuring its mass and a side. What is the maximum percentage error in the density if errors in measurement of a side and mass are 2% and 5% respectively?

a) 13%

b) 11%

c) 7%

d) 3%

Correct: b

Error Analysis

If p = 

\frac{x^{a}y^{b}}{z^c}
xaybzc\frac{x^{a}y^{b}}{z^c}

after measuring x, y, z with error

\triangle{x}, \triangle{y}, \triangle{z}
△x,△y,△z\triangle{x}, \triangle{y}, \triangle{z}

then percentage error =

(a * \frac{\triangle{x}}{x} + b * \frac{\triangle{y}}{y} + c* \frac{\triangle{z}}{z}) * 100
(a∗△xx+b∗△yy+c∗△zz)∗100(a * \frac{\triangle{x}}{x} + b * \frac{\triangle{y}}{y} + c* \frac{\triangle{z}}{z}) * 100

Density = 

\frac{m}{l^3}
ml3\frac{m}{l^3}

So, Error = 

(1 * \frac{\triangle{m}}{m} + 3 * \frac{\triangle{l}}{l} ) * 100
(1∗△mm+3∗△ll)∗100(1 * \frac{\triangle{m}}{m} + 3 * \frac{\triangle{l}}{l} ) * 100
(1 * 5 + 3 * 2 ) * 100 = 11
(1∗5+3∗2)∗100=11(1 * 5 + 3 * 2 ) * 100 = 11

= 

% 

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Unit and Dimension

By Roshan Bhandari

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