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}]
Dimension of Force =
Calculation of Dimension
[M]
Dimension of Force =
Mass * Acceleration
\frac{Velocity}{Time}
\frac{\frac{distance}{Time}}{Time}
=
=
[M]
[LT^{-2}]
*
=
[MLT^{-2}]
Calculation of Dimension
Dimension of Work=
Force * distance
=
[ML^{2}T^{-2}]
[MLT^{-2}]
[L]
Dimensional Formula of velocity gradient is
[M^0L^0T]
a)
[M^0L^0T^{-1}]
c)
[M^{-1}L^0T^0]
b)
[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}
so, h =
{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}
The dimensional constant of Current is
a)
Correct: b
b)
c)
d)
I = \frac{Q}{T}
[M^{0}L^{0}T^{1}Q^{-1}]
[M^{0}L^{0}T^{-1}Q^{1}]
[M^{0}L^{0}T^{-1}Q^{-1}]
[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}
\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}
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}]
Work = F*d = m*a*d =
[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}]
[M^{-1}L^{2}T^{-2}]
[M^{1}L^{-2}T^{-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}
% error = (measured value - actual value)/actual value *100
\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
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}
So, Error =
(1 * \frac{\triangle{l}}{l} ) * 100
(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}
So, Error =
(1 * \frac{\triangle{m}}{m} + 3 * \frac{\triangle{l}}{l} ) * 100
(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}}
So, Error =
(1 * \frac{\triangle{l}}{l} + 2 * \frac{\triangle{t}}{t} ) * 100
(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
Unit and Dimension Engineering
By Roshan Bhandari
