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.

In Astronomy , there is a unit of distance called A.U. - the astronomical unit. This denotes the distance between 

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

1 A.U = 1.496*10^11m

Unit

57cm

5 Kg

10 h 17m 40s

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

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]

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

Velocity Gradient = V/L

Plank’s constant has the dimension of[IOE]

a) Energy 

c) Frequency

b) Mass

d) Angular Momentum

Correct: d

Angular momentum =  mvr

E = hf = 

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

so, h = 

{mc}*{\lambda}
mc∗λ{mc}*{\lambda}

 = P

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}

The dimensional constant of Current is

a) 

Correct: b

b)

c)

d) 

I = \frac{Q}{T}
I=QTI = \frac{Q}{T}
[M^{0}L^{0}T^{1}Q^{-1}]
[M0L0T1Q−1][M^{0}L^{0}T^{1}Q^{-1}]
[M^{0}L^{0}T^{-1}Q^{1}]
[M0L0T−1Q1][M^{0}L^{0}T^{-1}Q^{1}]
[M^{0}L^{0}T^{-1}Q^{-1}]
[M0L0T−1Q−1][M^{0}L^{0}T^{-1}Q^{-1}]
[M^{0}L^{1}T^{-1}Q^{1}]
[M0L1T−1Q1][M^{0}L^{1}T^{-1}Q^{1}]

The dimension for 

a)  acceleration

Correct: b

b) Velocity

c) Time

d) Energy

\frac{1}{\sqrt{{\mu}_o}{\epsilon}_o}
1μoϵo\frac{1}{\sqrt{{\mu}_o}{\epsilon}_o}
\frac{1}{\sqrt{{\mu}_o{\epsilon}_o}}
1μoϵo\frac{1}{\sqrt{{\mu}_o{\epsilon}_o}}

are same as

Speed of light (c) = 

The dimension for stress is the same as

a) acceleration

Correct: b

b) Pressure

c) Force

d) Energy

\frac{F}{A}
FA\frac{F}{A}

Stress = 

The dimension  

a) Joule

Correct: a

b) Pascal

c) Newton

d) Watt

refers to a physical

quantity that has unit

[M^{1}L^{2}T^{-2}]
[M1L2T−2][M^{1}L^{2}T^{-2}]

Work = F*d = m*a*d =

[M^{1}L^{2}T^{-2}]
[M1L2T−2][M^{1}L^{2}T^{-2}]

Joule is the unit of Work or Energy

The dimension  

a)

Correct: d

b)

c) 

d) 

of modulus of rigidity is

[M^{1}L^{2}T^{-2}]
[M1L2T−2][M^{1}L^{2}T^{-2}]
[M^{-1}L^{2}T^{-2}]
[M−1L2T−2][M^{-1}L^{2}T^{-2}]
[M^{1}L^{-2}T^{-2}]
[M1L−2T−2][M^{1}L^{-2}T^{-2}]
[M^{1}L^{-1}T^{-2}]
[M1L−1T−2][M^{1}L^{-1}T^{-2}]

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 all dimensionless physical quantity may not be unit less.

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

Error Analysis

If p = 

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

% error = (measured value - actual value)/actual value *100

\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

and the error in x, y , z are

The error in the measurement of radius of a sphere is 1%, then the error in the measurement of volume is

a) 13%

b) 3%

c) 4%

d) 1%

Correct: b

Density = 

{l^3}
l3{l^3}

So, Error = 

(1 * \frac{\triangle{l}}{l} ) * 100
(1∗△ll)∗100(1 * \frac{\triangle{l}}{l} ) * 100
(1 * 3 ) * 100 = 3
(1∗3)∗100=3(1 * 3 ) * 100 = 3

= 

% 

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

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

= 

% 

In a certain measurement for acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of pendulum and 3% in the value of period. The maximum percentage error in the measurement of 'g' is 

a) 2%

b) 4%

c) 7%

d) 3%

Correct: c

g = 

4{\pi}^2 {\frac{l}{T^2}}
4π2lT24{\pi}^2 {\frac{l}{T^2}}

So, Error = 

(1 * \frac{\triangle{l}}{l} + 2 * \frac{\triangle{t}}{t} ) * 100
(1∗△ll+2∗△tt)∗100(1 * \frac{\triangle{l}}{l} + 2 * \frac{\triangle{t}}{t} ) * 100
(1 * 1 + 2 * 3 ) * 100 = 7
(1∗1+2∗3)∗100=7(1 * 1 + 2 * 3 ) * 100 = 7

= 

% 

The heat generated in a circuit given by Q = i^2Rt Joule where i is current, R is the resistance and t is time, if the percentage error in measuring i, R, t are 3%, 2% and 1% respectively then maximum error in measuring heat is

a) 9%

b) 12%

c) 6%

d) 18%

Correct: a

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