🔹 Topic: Fundamental and Derived Units | MCQs: 50 🔹
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1. Light year is a unit of
Correct answer: (c) Distance
A light year is the distance that light travels in one year in a vacuum. It's approximately 9.46 trillion kilometers.
2. The binding energy of a nucleon in a nucleus is of the order of a few [SCRA 1979]
Correct answer: (a) MeV
The binding energy per nucleon in a nucleus is typically in the range of 1-10 MeV (Mega electron Volts).
3. Which of the following is not equal to watt
Correct answer: (d) Ampere/volt
\[1 \text{ W} = 1 \text{ J/s} = 1 \text{ A} \times \text{V} = 1 \text{ A}^2 \times \Omega\]
Ampere/volt is the unit of conductance (Siemens), not power.
4. Newton-second is the unit of
Correct answer: (c) Momentum
\[\text{Momentum} = \text{mass} \times \text{velocity} = \text{kg} \cdot \text{m/s} = \text{N} \cdot \text{s}\]
Newton-second is the unit of impulse, which equals change in momentum.
5. Which of the following is not represented in correct unit
Correct answer: (d) Pressure = N/m³
The correct unit for pressure is Pascal (Pa) which is N/m², not N/m³.
6. One second is equal to
Correct answer: (d) 9192631770 time periods of Cs-133 clock
The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
7. One nanometre is equal to
Correct answer: (d) 10⁻⁹ m
\[1 \text{ nm} = 10^{-9} \text{ m} = 0.000000001 \text{ m}\]
The prefix "nano" means one billionth (10⁻⁹).
8. Which of the following pairs is wrong
Correct answer: (b) Relative density-Pyrometer
A pyrometer measures high temperatures, not relative density. Relative density is typically measured using a hydrometer.
9. The unit of power is
Correct answer: (c) Joule per second and watt both
\[1 \text{ W} = 1 \text{ J/s}\]
Both watt and joule per second are valid units for power.
10. A suitable unit for gravitational constant is
Correct answer: (a) N·m²/kg²
From Newton's law of gravitation:
\[F = G \frac{m_1 m_2}{r^2}\]
\[\Rightarrow G = \frac{F r^2}{m_1 m_2}\]
Thus the units are N·m²/kg².
11. SI unit of pressure is
Correct answer: (a) Pascal
The SI unit of pressure is Pascal (Pa), which is equivalent to N/m² or kg/m·s². Atmosphere is a non-SI unit.
12. The unit of angular acceleration in the SI system is
Correct answer: (c) rad/s²
Angular acceleration is the rate of change of angular velocity (rad/s) with respect to time (s), so its unit is rad/s².
13. The unit of Stefan's constant σ is
Correct answer: (a) W/m²·K⁴
From Stefan-Boltzmann law:
\[P = \sigma A T^4\]
\[\Rightarrow \sigma = \frac{P}{A T^4}\]
Thus the units are W/m²·K⁴.
14. Which of the following is not a unit of energy
Correct answer: None (all are units of energy)
All options are valid units of energy:
\[1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\]
\[1 \text{ eV} = 1.602 \times 10^{-19} \text{ J}\]
\[1 \text{ N} \cdot \text{m} = 1 \text{ J}\]
Joule is the SI unit of energy.
15. In \(y = A \sin(\omega t - kx)\), \(x\) is measured in metres and \(t\) in seconds. The unit of \(k\) is
Correct answer: (c) m⁻¹
The argument of the sine function must be dimensionless. Since \(kx\) must be dimensionless and \(x\) has units of meters:
\[[k] \cdot \text{m} = \text{dimensionless} \Rightarrow [k] = \text{m}^{-1}\]
16. A cube has numerically equal volume and surface area. The volume of such a cube is
Correct Answer: (a) 216 units
For a cube with side length 's':
Volume = s³
Surface Area = 6s²
Given that Volume = Surface Area numerically:
s³ = 6s² ⇒ s = 6
Therefore, Volume = 6³ = 216 units
Volume = s³
Surface Area = 6s²
Given that Volume = Surface Area numerically:
s³ = 6s² ⇒ s = 6
Therefore, Volume = 6³ = 216 units
17. Wavelength of ray of light is \( \lambda \). It is equal to
Correct Answer: (a) \( \frac{hc}{E} \)
From Planck's equation: \( E = h\nu \)
And \( \nu = \frac{c}{\lambda} \)
Therefore: \( E = \frac{hc}{\lambda} \) ⇒ \( \lambda = \frac{hc}{E} \)
And \( \nu = \frac{c}{\lambda} \)
Therefore: \( E = \frac{hc}{\lambda} \) ⇒ \( \lambda = \frac{hc}{E} \)
18. Electron volt is a unit of
Correct Answer: (d) Energy
An electron volt (eV) is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. It is a unit of energy.
19. Unit of power is
Correct Answer: (a) Kilowatt
Power is the rate of doing work, measured in watts (W). Kilowatt (kW) is a larger unit of power (1000 W). Kilowatt-hour is a unit of energy, dyne is a unit of force, and joule is a unit of energy.
20. Unit of energy is
Correct Answer: (a) \( \text{kg}\, \text{m}^2 \text{s}^{-2} \)
Energy (in joules) has dimensions of force × distance = (mass × acceleration) × distance = \( \text{kg} \times \text{m/s}^2 \times \text{m} = \text{kg}\, \text{m}^2 \text{s}^{-2} \).
21. Volt/metre is the unit of
Correct Answer: (d) Electric intensity
Electric field intensity (or electric field strength) is defined as the force per unit charge, which has units of newtons per coulomb (N/C). Since 1 V = 1 J/C and 1 J = 1 N·m, we get 1 N/C = 1 V/m.
22. \( \text{kg}\, \text{m}\, \text{s}^{-1} \) is the unit of
Correct Answer: (b) Momentum
Momentum (p) is defined as mass × velocity, which has units of kg × m/s = \( \text{kg}\, \text{m}\, \text{s}^{-1} \).
23. The unit of reduction factor of tangent galvanometer is
Correct Answer: (a) Ampere
The reduction factor (K) of a tangent galvanometer is the current required to produce a deflection of 45°, and thus has units of ampere.
24. The unit of self inductance of a coil is
Correct Answer: (b) Henry
The SI unit of self-inductance is the henry (H), named after Joseph Henry. 1 H = 1 Wb/A.
25. Henry/ohm can be expressed in
Correct Answer: (a) Second
Since henry (H) = Ω·s (ohm-second), then H/Ω = s (seconds).
26. The SI unit of momentum is
Correct Answer: (a) \( \text{kg}\, \text{m}\, \text{s}^{-1} \)
Momentum = mass × velocity. The SI unit of mass is kg and of velocity is m/s, so the SI unit of momentum is kg·m/s.
27. The velocity of a particle depends upon as \( v = \sqrt{a + bt} \); if the velocity is in m/s, the unit of a will be
Correct Answer: (a) \( \text{m}^2 \text{s}^{-2} \)
For the equation to be dimensionally consistent, 'a' must have the same units as v² (since it's under square root). So units of a = (m/s)² = m²/s².
28. Which of the following represents a volt
Correct Answer: (b) Watt/Ampere
Since V = W/A (volts = watts/amperes). Also correct is J/C (joule/coulomb), but that's not among the options.
29. \( \text{kg}\, \text{m}^2 \text{s}^{-3} \text{A}^{-1} \) is a unit of
Correct Answer: (c) Power
These are the fundamental units for voltage (V), since V = J/(A·s) and J = kg·m²/s², so V = kg·m²/(A·s³).
30. What is the SI unit of permeability
Correct Answer: (d) All the above units are correct
All these are equivalent units for magnetic permeability (μ₀):
1 H/m = 1 T·m/A = 1 Wb/(A·m)
1 H/m = 1 T·m/A = 1 Wb/(A·m)
31. Tesla is a unit for measuring
Correct Answer: (b) Magnetic induction
The tesla (T) is the SI unit of magnetic flux density (also called magnetic induction), defined as 1 T = 1 Wb/m².
32. If the unit of length and force be increased four times, then the unit of energy is
Correct Answer: (c) Increased 16 times
Energy = Force × Distance
If both force and distance units increase by 4 times, then energy unit increases by 4 × 4 = 16 times.
If both force and distance units increase by 4 times, then energy unit increases by 4 × 4 = 16 times.
33. Oersted is a unit of
Correct Answer: (b) Magnetic intensity
The oersted (Oe) is the CGS unit of magnetic field strength (H-field). 1 Oe = 1000/(4π) A/m ≈ 79.577 A/m.
34. \( \text{A}\, \text{s} \) is a unit of
Correct Answer: (a) Quantity of electricity
Ampere-second (A·s) is the unit of electric charge (coulomb). It represents quantity of electricity.
35. \( \text{rad}\, \text{s}^{-1} \) is a unit of
Correct Answer: (b) Velocity
Radians per second (rad/s) is the unit of angular velocity, which is analogous to linear velocity but for rotational motion.
36. If \( u_1 \) and \( u_2 \) are the units selected in two systems of measurement and \( n_1 \) and \( n_2 \) their numerical values, then
Correct Answer: (a) \( n_1u_1 = n_2u_2 \)
The physical quantity remains the same in both systems, so the product of numerical value and unit must be equal: \( n_1u_1 = n_2u_2 \).
37. \( 10^7 \) erg is
Correct Answer: (a) Same as one joule
1 J = 10⁷ erg. The erg is the CGS unit of energy, while joule is the SI unit.
38. \( \text{N}\, \text{m}^{-1} \)
Correct Answer: (d) Represents force per unit length
N/m represents force per unit length, such as surface tension which has units of N/m.
39. The nuclear cross-section is measured in barn, it is equal to
Correct Answer: (c) \( 10^{-28} \text{m}^2 \)
1 barn = 10⁻²⁸ m². This unit is used to measure the cross-sectional area of atomic nuclei.
40. Unit of magnetic moment is
Correct Answer: (a) \( \text{A}\, \text{m}^2 \)
Magnetic moment = current × area, so its units are ampere × meter² (A·m²).
41. Curie is a unit of
Correct Answer: (c) Radioactivity
The curie (Ci) is a unit of radioactivity, defined as 3.7×10¹⁰ decays per second (the activity of 1 gram of radium-226).
42. Hertz is the unit for
Correct Answer: (a) Frequency
The hertz (Hz) is the SI unit of frequency, defined as one cycle per second.
43. In SI, Henry is the unit of
Correct Answer: (c) (a) and (b) both
The henry (H) is the SI unit for both self-inductance and mutual inductance.
44. Young's modulus of a material has the same units as
Correct Answer: (a) Pressure
Young's modulus = Stress/Strain. Since strain is dimensionless, Young's modulus has the same units as stress (pressure), which is N/m² or pascal (Pa).
45. One yard in SI units is equal
Correct Answer: (b) 0.9144 m
1 yard = 3 feet = 36 inches = 0.9144 meters exactly.
47. Which of the following is smallest unit
Correct Answer: (c) Fermi
Fermi (fm) = 10⁻¹⁵ m (used for nuclear sizes)
Angstrom (Å) = 10⁻¹⁰ m (atomic scales)
Millimeter (mm) = 10⁻³ m
Meter is the base unit.
Angstrom (Å) = 10⁻¹⁰ m (atomic scales)
Millimeter (mm) = 10⁻³ m
Meter is the base unit.
48. The units of modulus of rigidity are
Correct Answer: (c) \( \text{N}\, \text{m}^{-2} \)
Modulus of rigidity (shear modulus) = shear stress/shear strain. Stress has units of N/m² (same as pressure).
49. The unit of absolute permittivity is
Correct Answer: (b) Farad/meter
Absolute permittivity (ε) has units of farads per meter (F/m). This comes from the capacitance formula C = εA/d, where A is area and d is distance.
50. Which relation is wrong
Correct Answer: (d) \( 1\, \text{fermi} = 10^{-13}\, \text{m} \)
1 fermi = 1 femtometer = 10⁻¹⁵ m, not 10⁻¹³ m. The other relations are correct:
1 cal ≈ 4.18 J
1 Å = 10⁻¹⁰ m
1 micron = 1 μm = 10⁻⁶ m
1 cal ≈ 4.18 J
1 Å = 10⁻¹⁰ m
1 micron = 1 μm = 10⁻⁶ m
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