Introduction to Physics
OBJECTIVE - I
OBJECTIVE - I
1. Which of the following sets cannot enter into the list of fundamental quantities in any system of units?
(a) length, mass, and velocity,
(b) length, time and velocity,
(c) mass, time and velocity,
(d) length, time and mass.
ANSWER: (b).
EXPLANATION: Two qualities of fundamental quantities are,
(a) The fundamental quantities should be independent of each other. In (b) velocity is dependent on length and time.
(b) All other quantities may be expressed in terms of the fundamental quantities. But in (b), the mass of an object can not be expressed in these terms.
2. A physical quantity is measured and the result expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then
(a) n ∝ size of u
(b) n ∝ u²
(c) n ∝ √u
(d) n ∝ 1/u.
ANSWER: (d).
EXPLANATION: Bigger the unit smaller will be the numerical value 'n'. So n is inversely proportional to the size of the unit. i.e. n*u = constant. For example, a distance of 5 km can be expressed as 5000 m, 500000 cm, 5000000 mm.
5000 m = 5000* 1/1000 km = 5 km
500000 cm = 500000* 1/100000 km = 5 km
5000000 mm = 5000000* 1/1000000 km = 5 km.
3. Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is [x] = MaLbTc. The quantity mass
(a) can always be dimensionally represented in terms of L, T, and x,
(b) can never be dimensionally represented in terms of L, T, and x,
(c) maybe represented in terms of L, T, and x if a = 0.
(d) maybe represented in terms of L, T, and x if a ≠ 0.
ANSWER: (d).
EXPLANATION: If a = 0, then the quantity has no mass component, hence it cannot be represented in terms of L, T, and x. If a ≠ 0, then it has a mass component and it can be expressed in terms of L, T, and x. So the option (d) is true.
4. A dimensionless quantity
(a) never has a unit,
(b) always has a unit,
(c) may have a unit
(d) does not exist.
ANSWER: (c).
EXPLANATION: A dimensionless quantity may or may not have a unit. For example, the angle has a unit as radian, but it is a dimensionless quantity while specific gravity is also dimensionless but unitless. Hence the option (c).
5. A unitless quantity
(a) never has a nonzero dimension,
(b) always has a nonzero dimension,
(c) may have a nonzero dimension,
(d) does not exist.
ANSWER: (a).
EXPLANATION: A unitless quantity is also dimensionless. Hence it can never have a nonzero dimension.
6. ∫ dx/√(2ax-x²) = aⁿ sin⁻¹[x/a - 1].
The value of n is
(a) 0,
(b) -1,
(c) 1,
(d) non of these.
You may use dimension analysis to solve the problem.
ANSWER: (a).
EXPLANATION: We assume x as length, hence x has dimensions = [L]. The whole term Sin⁻¹(x/a - 1) is an angle (radian) hence it is dimensionless. In this (x/a - 1) is the ratio (Sine) hence dimensionless, thus x and a must-have the same dimension that of L. Now,
[∫ dx/√(2ax-x²)] = [L/√L²] =[L⁰] and
[aⁿ Sin⁻¹(x/a -1)] = [Lⁿ]
Equating the dimensions of both sides,
[L⁰] = [Lⁿ]
→n = 0.
Hence the option (a).
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Links to the Chapters
Links to the Chapters
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 8 - Work and Energy
Click here for → Question for Short Answers
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → Exercises (1-10)
Click here for → Question for Short Answers
Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → Exercises (1-10)
Click here for → Exercises (11-20)
Click here for → Exercises (21-30)
Click here for → Exercises (31-42)
Click here for → Exercise(43-54)
Click here for → Exercises (21-30)
Click here for → Exercises (31-42)
Click here for → Exercise(43-54)
CHAPTER- 7 - Circular Motion
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Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → EXERCISES (11-20)
Click here for → EXERCISES (21-30)
CHAPTER- 6 - Friction
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Click here for → OBJECTIVE-I
Click here for → OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → EXERCISES (11-20)
Click here for → EXERCISES (21-30)
CHAPTER- 6 - Friction
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Click here for → Questions for Short Answer
Click here for → OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → Exercises (11-20)
Click here for → EXERCISES (21-31)
Click here for → OBJECTIVE-I
Click here for → Friction - OBJECTIVE-II
Click here for → EXERCISES (1-10)
Click here for → Exercises (11-20)
Click here for → EXERCISES (21-31)
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CHAPTER- 5 - Newton's Laws of Motion
Click here for → QUESTIONS FOR SHORT ANSWER
Click here for → QUESTIONS FOR SHORT ANSWER
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→ Newton's laws of motion - Objective - I
Click here for → Newton's Laws of Motion - Objective -II
Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)
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CHAPTER- 4 - The Forces
The Forces-
"Questions for short Answers"
Click here for "The Forces" - OBJECTIVE-I
Click here for "The Forces" - OBJECTIVE-II
Click here for "The Forces" - Exercises
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CHAPTER- 3 - Kinematics - Rest and Motion
Click here for "Questions for short Answers"
Click here for "OBJECTIVE-I"
Click here for EXERCISES (Question number 1 to 10)
Click here for EXERCISES (Question number 11 to 20)
Click here for EXERCISES (Question number 21 to 30)
Click here for EXERCISES (Question number 31 to 40)
Click here for EXERCISES (Question number 41 to 52)
CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
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