GameChanger Academy

Mechanics

1. Units, Dimensions and Errors

2. Vectors and Scalars

3. Motion in a Straight Line

4. Projectile Motion

5. Newton's Laws of Motion

6. Friction

7. Work, Energy, Power and Collision

8. Circular motion

9. Rotational motion

10. Simple Harmonic Motion

11. Gravitation

12. Elasticity

13. Surface Tension

14. Fluid dynamics and Viscosity

15. Hydrostatics

Heat and Thermodynamics

16. Thermometry

17. Thermal expansion

18. Calorimetry, Change of State and Hygrometry

19. Gas Laws and Kinetic theory of Gases

20. Transmission of Heat

21. Thermodynamics

Sound and Waves

22. Wave

23. Superposition of Waves

24. Stationary/ Standing waves

25. Doppler's effect and Musical sound

Optics

26. Reflection of Plane and Curved Mirrors

27. Refraction at Plane surfaces and Total internal reflection

28. Refraction through prism and Dispersion of Light

29. Refraction through Lenses

30. Chromatic abberation in Lenses, Optical instruments and Human eye

31. Velocity of Light

32. Photometry

33. Wave nature of Light

Electrostatics

34. Charge and Force

35. Electric Field and Potential

36. Capacitance

Electrodynamics

37. Electric current

38. Heating Effect of Current

39. Thermoelectricity

40. Chemical effect of Current

41. Meters

Electromagnetism

42. Properties of Magnets

43. Magnetic effects of Current

44. Electromagnetic induction

45. Alternating current

Modern Physics

46. Cathode rays, Positive rays and Electrons

47. Photoelectric effect

48. X-rays

49. Atomic structure and Spectrum

50. Radioactivity

51. Nuclear physics

52. Semiconductor and Semiconductor devices

53. Diode and Triode valves

54. Logic gates

55. Relativity and Universe

56. Particle physics

Mechanics

1. Units, Dimensions and Errors

FUNDAMENTAL UNITS

S.N.	Physical Quantity	Symbol for Physical quantity	Name of Units	Symbol for Unit
1.	Length	L	metre	m
2.	Mass	M	kilogram	kg
3.	Time	T	second	s
4.	Electric current	I	Ampere	A
5.	Temperature	θ	kelvin	K
6.	Luminous intensity	J	candela	cd
7.	Amount of substance	N	mole	mol

SUPPLEMETNAL BASE UNITS

S.N.	Physical quantity	Symbol for Physical quantity	Name of Units	Symbol for Unit
1.	Angle		Radian	rad
2.	Solid angle		Steradian	sr

DERIVED UNITS

S.N.	Physical Quantity	Formula	Dimensions
1.	Area	Length × Length	[L²]
2.	Volume	Length³	[L³]
3.	Density	Mass / Volume	[ML⁻³]
4.	Velocity	Displacement / Time	[LT⁻¹]
5.	Acceleration	Velocity / Time	[LT⁻²]
6.	Momentum	Mass × Velocity	[MLT⁻¹]
7.	Force	Mass × Acceleration	[MLT⁻²]
8.	Impulse	Force × Time	[MLT⁻¹]
9.	Work / Energy	Force × Displacement	[ML²T⁻²]
10.	Power	Work / Time	[ML²T⁻³]
11.	Pressure	Force / Area	[ML⁻¹T⁻²]
12.	Stress	Force / Area	[ML⁻¹T⁻²]
13.	Strain	ΔLength / Original Length	Dimensionless
14.	Young’s Modulus	Stress / Strain	[ML⁻¹T⁻²]
15.	Surface Tension	Force / Length	[MT⁻²]
16.	Viscosity (η)	Stress / Velocity Gradient	[ML⁻¹T⁻¹]
17.	Angular Displacement	θ (arc length / radius)	Dimensionless
18.	Angular Velocity	θ / Time	[T⁻¹]
19.	Angular Acceleration	Angular velocity / Time	[T⁻²]
20.	Moment of Inertia	Mass × Radius²	[ML²]
21.	Torque	Force × Perpendicular distance	[ML²T⁻²]
22.	Angular Momentum	Moment of inertia × Angular velocity	[ML²T⁻¹]
23.	Frequency	1 / Time	[T⁻¹]
24.	Wavelength	Wave speed / Frequency	[L]
25.	Wave number	1 / Wavelength	[L⁻¹]
26.	Wave speed	Wavelength × Frequency	[LT⁻¹]
27.	Energy density	Energy / Volume	[ML⁻¹T⁻²]
28.	Heat	Work (Joule equivalent)	[ML²T⁻²]
29.	Temperature gradient	Δθ / Length	[L⁻¹θ]
30.	Thermal conductivity	Heat flux × Length / (ΔT × Time)	[MLT⁻³θ⁻¹]
31.	Gravitational potential	Work / Mass	[L²T⁻²]
32.	Gravitational field intensity	Force / Mass	[LT⁻²]
33.	Gravitational constant (G)	F r² / (m₁m₂)	[M⁻¹L³T⁻²]
34.	Electric charge	Current × Time	[IT]
35.	Electric field	Force / Charge	[MLT⁻³I⁻¹]
36.	Electric potential	Work / Charge	[ML²T⁻³I⁻¹]
37.	Potential gradient	Electric potential / Length	[MLT⁻³I⁻¹]
38.	Capacitance	Charge / Potential	[M⁻¹L⁻²T⁴I²]
39.	Resistance	Potential difference / Current	[ML²T⁻³I⁻²]
40.	Resistivity	Resistance × Area / Length	[ML³T⁻³I⁻²]
41.	Conductivity	1 / Resistivity	[M⁻¹L⁻³T³I²]
42.	Electric power	Current × Voltage	[ML²T⁻³]
43.	Magnetic flux	Magnetic field × Area	[MT⁻²I⁻¹L²]
44.	Magnetic flux density (B)	Force / (Charge × Velocity)	[MT⁻²I⁻¹]
45.	Permeability	B × Length / Current	[MLT⁻²I⁻²]
46.	Inductance	Magnetic flux / Current	[ML²T⁻²I⁻²]
47.	Self-inductance	Induced emf × Time / Current	[ML²T⁻²I⁻²]
48.	Mutual inductance	Flux linkage / Current in other coil	[ML²T⁻²I⁻²]
49.	Emf	Work / Charge	[ML²T⁻³I⁻¹]
50.	Luminous flux	Luminous intensity × Solid angle	[J]
51.	Illuminance	Luminous flux / Area	[J L⁻²]
52.	Radiant flux	Energy / Time	[ML²T⁻³]
53.	Radiant intensity	Power / Solid angle	[ML²T⁻³ sr⁻¹]
54.	Specific heat capacity	Heat / (Mass × ΔT)	[L²T⁻²θ⁻¹]
55.	Entropy	Heat / Temperature	[ML²T⁻²θ⁻¹]
56.	Coefficient of Thermal expansion	ΔL / (L ΔT)	[θ⁻¹]
57.	Planck’s constant	Energy / Frequency	[ML²T⁻¹]
58.	Stefan-Boltzmann constant	Power / (Area × T⁴)	[MT⁻³θ⁻⁴]
59.	Universal gas constant	PV / nT	[ML²T⁻²θ⁻¹mol⁻¹]
60.	Boltzmann constant	R / NA	[ML²T⁻²θ⁻¹]

PREFIXES FOR POWER OF 10

Power of 10	Prefix	Symbol
10²⁴	yotta	Y
10²¹	zetta	Z
10¹⁸	exa	E
10¹⁵	peta	P
10¹²	tera	T
10⁹	giga	G
10⁶	mega	M
10³	kilo	k
10²	hecto	h

10¹	deca	da
10^-1	deci	d
10^-2	centi	c
10^-3	milli	m
10^-6	micro	μ
10^-9	nano	n
10^-12	pico	p
10^-15	femto	f
10^-18	atto	a
10^-21	zepto	z
10^-24	yocto	y

1. 1 torrr is

[BP 2014]

1 atm
1 mm of Hg
1 barr
1 cm of Hg

2. What is the dimension of capacitance?

[BP 2013]

[M^-1L²T^-3A^-2]
[LT^-4]
[M^-1L^-2T⁴A²]
[ML²T^-4A^-2]

3. Dimension of which are same

[BP 2013]

Work and moment of force
Torque and force
Velocity and velocity gradient
All

4. Dimension of universal gas constant is:

[]

[ML²T²K^-1mol^-1]
[ML²T^-2K^-1]
[ML²T^-2K^-1mol^-2]
[ML²T^-2mol]

5. The least count is 0.01 mm. Two wires of length L_{1 and L² are measured and they are connected forming a single wire. Then the measurements is:}

[BP 2012]

(L₁ + L₂) m ± 0.02 mm
(L₁ + L₂) m ± 0.01 mm
(L₁ - L₂) m ± 0.02 mm
(L₁ - L₂) m ± 0.01 mm

6. The dimension of Boltzmann's constant is:

[BP 2011]

[ML²T²K^-1]
[ML²T²K¹]
[ML^-2T^-2K^-1]
[ML³T²K¹]

7. The dimensional formula for coefficient of viscosity is

[]

[ML²T^-2]
[ML^-1T¹]
[ML^-1T¹]
[ML²T^-1]

8. In a micrometer gauge the reading is done by rotating terminal screw on account of worn out threads on circular scale in sam esense to prevent:

[]

zero error
Instrumental error
Back-lash error
Absolute erro

9. If force, length and time are taken a fundamental unit then the dimension of mass will be:

[MOE 2014]

[FL¹T^-2]
[F⁰L⁰T^-2]
[F¹L²T^-2]
[F¹L^-1T²]

10. Inductance divided by resistance will have the unit:

[MOE 2014]

Ampere/sec
Volt/sec
Per sec
Sec

11. Planck's constant has the dimension of:

[MOE 2013, 2012]

Energy
Mass
Frequency
Angular momentum

12. Dimension of torque is::

[MOE 2012]

[ML²T²]
[ML²T^-2]
[ML²T]
[MLT¹]

13. Dimension of moment of inertia of a body::

[MOE 2011]

[ML^-2T^-1]
[ML²T⁰]
[M²L²T⁰]
[MLT¹]

14. Dimension of Inductance::

[MOE 2011]

[ML²T^-2A^-2]
[ML²T^-2A^-1]
[M²L²T^-3A^-2]
[MLA^-1]

15. The coefficient of thermal conductivity is expressed in the unit

[MOE 2010]

Watt (Kelvin per meter)
Joule per Kelvin per meter per second
Watt (meter per kelvin)
Joule (Kelvin per meter per second)

16. Dimension of Work is same as

[KU 2014]

Torque
Force
Power
All

17. Which of the following pairs of physical quantities has the same dimension?

[KU 2012]

Power and Energy
Work and Energy
Force and Momentum
Energy and Momentum

18. The dimension of which of the following has [ML^-1T^-1]

[KU 2013]

Angular momentum
Force
Surface tension
Viscosity

19. Dimension of the stress

[I.E. 2010]

[ML^-2T^-2]
[ML^-1T^-2]
[ML²T²]
[ML¹T²]

20. Candela is the unit of

[I.E. 2012]

Intensity of flame
Amount of substance
Level of Sound
None

21. 1 Watt second is equal to

[I.E. 2012]

N/M
Nm/Kg
Joule
Joule/Second

22. Find out the dimension of K in the equation: W = 1/2 kx²

[I.E. 2013]

[ML⁰T^-2]
[ML⁰T^-1]
[M⁰LT^-1]
[ML^-1T^-2]

23. If energy E, velocity V and time T are taken as fundamental units, the dimensional formula for surface tension becomes

[]

[EV^-2T^-2]
[E⁰V^-2T^-2]
[E²V²T^-2]
[EV^-2T²]

24. Which of the following system of units cannot enter into fundamental units?

[]

Length, Mass and Time
Velocity, Frequency and Acceleration
Energy, Force and Density
Volume, Time period and Moment of inertia

25. What are the dimensions of angular displacement?

[]

[L]
[M⁰LT^-1]
[L²
None

26. The position x of a particle at time t is given by x = b/a (1-e^at) where a and b are non-zero constants. The dimensions of b are

[]

[M⁰LT²]
[M⁰LT⁰]
[M⁰L⁰T^-1]
[M⁰LT^-1]

27. In Vander Waal's equation (P + a/V^2)(V-b) = RT, the dimension of 'a' are

[]

[ML⁵T^-2]
[ML³T^-1]
[M⁰L⁶T⁰]
[ML⁷T^-2]

28. The unit of Stefan's Boltzmann contant σ is

[]

Watt/ (m.K^4)
Calorie/ (m^2.K^4)
Watt/ (m^2.K^4)
Joule/ (m^2.K^4)

29. Which of the following have same dimension

[]

Angular momentum and linear momentum
Work and Power
Work and Torque
Torque and Pressure

30. Which of the following is a correct unit of gravitational constant?

[MOE-2009]

[m³kg^-2s^-2]
[m³kg^-2s^-1]
[m^-3kg^-1s²]
[m^-3kg²s^-1]

31. Dimension of Angstrom (A), Micron (μ), Fermi (F) and Nanometer (nm) is the same. Which one of the following represent the correct arrangement of their magnitude in the decreasing order?

[MOE-2009]

μ, A, nm, F
A, μ, F, nm
F, A, nm, μ
μ, nm, A, F

32. S.I unit equivalent to the magnetic field Tesla (T) may be

[MOE-2009]

V sm²
V sm^-2
V s^-1m²
V^-1 sm^-2

33. The dimensional formula or coefficient of viscosity is

[KU-2010/MOE]

[ML^-1T^-1]
[ML⁰T⁰]
[ML^-2T¹]
[ML^-1T¹]

34. NC^-1 has the same dimension as

[KU 2009]

Volt meter
Farad meter
Farad/meter
Volt/meter

35. The dimensional formula of impulse is

[KU 2009]

[MLT^-2]
[MLT^-1]
[ML²T^-1]
[M²LT^-1]

36. The star nearest to earth is 4 light years away. The distance is ......

9.46 x 10^15 m
37.84 x 10^12 m
37.84 x 10^15 m
9.5 x 10^12 m

37. The dimensions of angular momentum are:

[IOM 96]

[MLT^-1]
[ML²T^-1]
[ML^-1T]
[MLT^-2]

38. The dimensional formula for stress is the same as that for

[MOE 066]

force
pressure
torque
work

39. Dimension of permittivity of free space (ε₀) is

[MOE 2066]

[M^-1L³T⁴A²]
[M^-1L^-3T⁴A²]
[M^-1L^-3T^-4A²]
[M^-1L^-3T⁴A]

40. The dimension of Universal Gravitational constant is

[ML^-1T^-2]
[M^-1L²T^-2]
[M^-1L²T^-2]
[M⁰L^-1T^-2]

41. The dimension of velocity gradient is the same as that of

[MOE 2065]

time period
acceleration
angular velocity
frequency

42. If unit of force and length are doubled, then unit of power becomes:

[MOE 2063]

six times
four times
2 times
none

43. The dimension (M¹L²T^-2) refers to a physical quantity that has unit:

[MOE 2063]

Joule
Pascal
Newton
Watt

44. The dimensional formula for Plank's constant is

[MOE 2063/ BP 2016]

[M¹L²T^-1]
[M¹L²T²]
[MLT^-2]
[M²L²T^-1]

45. The diameter of nucleus is of order of

[MOE 2063]

10^-12 cm
10^-11 cm
10^-13 cm
10^-10 cm

46. The unit of ε_o, the absolute permitivity of free space are

[MOE 2062]

CV^-1m^-1 {C -> coulomb}
CA^-1m^-1
C^-2m^-2
Fm

47. The dimension of current is:

[MOE 2062]

[M⁰L⁰TQ^-1]
[M⁰L⁰T^-1Q]
[M⁰LT¹Q^-1]
[M⁰L⁰T¹Q^-1]

48. The dimensional formula for kinetic energy is:

[MOE 2010]

[M⁰L²T^-2]
[ML²T^-1]
[MLT^-1]
[ML²T^-2]

49. Which of the following have same dimension?

[MOE 2061]

power and energy
linear momentum & torque
linear momentum & impulse
torque & power

50. [ML²T³I^-1] is a unit of

[MOE 2056]

resistivity
electric field
potential difference
capacitance

51. 'Light year' is the unit of

[MOE 2056]

Length
Velocity
Time
Momentum

52. The S.I. unit of electric field

[IE 2007]

N/C^2
NM/C
NM^2/C
C/Nm

53. The dimensional of modulus of rigidity is:

[BPKIHS - 08]

[ML^-2T^-2]
[MLT^-2]
[ML^-1T^-1]
[ML^-1T^-2]

54. Weight of milky way galaxy is

4 x 10 ^41 kg
3 x 10^41 kg
6 x 10^41 kg
7 x 10 ^ 41 kg

55. Which is not a unit of length?

[BPKIHS 02]

Parsec
Light year
Debye
Angstrom

56. The pair NOT having identical dimensions is:

[BPKIHS-03]

Impulse and Linear momentum
Plank's constant and angular momentum
Moment of inertia and moment of force
Young's modulus and pressure

57. The dimension of E/B is same as that of

[BPKIHS-04]

velocity
momentum
force
acceleration

58. If the current in electric bulb drops by one percent the power decreases by:

[BPKIHS 05]

10%
2%
1/2 %
4%

59. Which of the relation is correct from dimensional point of view?

[BPKIHS-94]

v² = u² + 2 as
v² = u² + 2 as²
v² = u² + 2 a²s
None

60. 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 the errors in the measurement of side and mass are 3% and 4% respectively.

[BPKIHS 1995]

61. In Astronomy, there is a unit of distance called AU. The astronomical unit. This denotes the distance between

[BPKIHS 1995]

The sun and Earth
The sun and the planet Mercury
The Moon and Earth
The two poles of Earth (its diameter)

62. The dimensional formula of surface tension is

[MLT^-1]
[MLT^-2]
[ML⁰T^-2]
[ML^-1T¹]

63. The term 'light year' is used for

the time taken for light to travel from the sun to the earth
the unit of distance light travels in a year
the particular year that the light intensity is maximum
the time taken for light to travel from the nearest star to the earth

64. If the radius of earth were to decrease by 1%, its mass remaining the same, the acceleration due to gravity on the surface of the earth will

increase by 1%
decrease by 2%
decrease by 1%
increase by 2%

65. Coefficient of viscosity (η) has the dimension Nm^-2S. It is equivalent to

[IOM 2015]

Pascal second
Decipoise
Centipoise
Millipoise

66. e²/εhc has dimension of

[IOM 2016]

Time
Length
Mass
Dimensionless

67. The unit of Resistance in SI system is

[KU 2016]

kg m² sec^-2 A^-1
kg m² sec^-3 A^-2
kg m² sec^-3 A^-1
kg m² sec^-2 A^-1

68. The dimension ML^-1T^-2 corresponds to:

[KU 2017]

Work done by force
Pressure
Linear momentum
Coefficient of viscosity