Units and Measurements- Assignment

Class 11 Physics Assignment

Chapter: Units and Measurements

Q1. The dimensional formula of force is:

A) [MLT⁻¹]

B) [MLT⁻²]

C) [ML²T⁻²]

D) [M⁰LT⁻²]

View Solution
Force = mass × acceleration.

Mass = [M], acceleration = [LT⁻²].

Therefore force = [MLT⁻²].
Answer: B

Q2. The SI unit of pressure is:

A) Newton

B) Joule

C) Pascal

D) Watt

View Solution
Pressure = Force / Area.

SI unit = N/m² = Pascal.
Answer: C

Q3. Which of the following is a fundamental quantity?

A) Force

B) Work

C) Length

D) Pressure

View Solution
Length is a fundamental physical quantity. Force, work and pressure are derived quantities.
Answer: C

Q4. The dimensional formula of work is:

A) [MLT⁻²]

B) [ML²T⁻²]

C) [ML²T⁻¹]

D) [M²LT⁻²]

View Solution
Work = Force × displacement = [MLT⁻²][L] = [ML²T⁻²].
Answer: B

Q5. The number of significant figures in 0.00450 is:

A) 2

B) 3

C) 4

D) 5

View Solution
Leading zeros are not significant. 4, 5 and final zero after decimal are significant.

Total significant figures = 3.
Answer: B

Q6. The dimensional formula of power is:

A) [ML²T⁻²]

B) [ML²T⁻³]

C) [MLT⁻³]

D) [M⁰L²T⁻³]

View Solution
Power = Work / Time = [ML²T⁻²]/[T] = [ML²T⁻³].
Answer: B

Q7. The least count of a vernier caliper is given by:

A) 1 MSD + 1 VSD

B) 1 MSD − 1 VSD

C) 1 VSD − 1 MSD

D) MSD × VSD

View Solution
Least count = 1 main scale division − 1 vernier scale division.
Answer: B

Q8. If percentage errors in length, breadth and height are 1%, 2% and 3%, percentage error in volume is:

A) 1%

B) 2%

C) 3%

D) 6%

View Solution
Volume V = lbh.

Percentage error in product = sum of percentage errors = 1 + 2 + 3 = 6%.
Answer: D

Q9. Which of the following has dimensions of impulse?

A) Force

B) Momentum

C) Work

D) Power

View Solution
Impulse = Force × Time = [MLT⁻²][T] = [MLT⁻¹], same as momentum.
Answer: B

Q10. The SI unit of solid angle is:

A) Radian

B) Steradian

C) Degree

D) Candela

View Solution
The SI unit of solid angle is steradian.
Answer: B

Q11. The dimensional formula of density is:

A) [ML⁻³]

B) [ML³]

C) [M⁻¹L³]

D) [ML⁻²]

View Solution
Density = Mass / Volume = [M]/[L³] = [ML⁻³].
Answer: A

Q12. The unit of gravitational constant G is:

A) N kg² m⁻²

B) N m² kg⁻²

C) N m kg⁻¹

D) N kg m⁻²

View Solution
From F = Gm₁m₂/r², G = Fr²/(m₁m₂).

Unit = N m² kg⁻².
Answer: B

Q13. The dimensional formula of G is:

A) [M⁻¹L³T⁻²]

B) [ML³T⁻²]

C) [M⁻¹L²T⁻²]

D) [M⁻²L³T⁻²]

View Solution
G = Fr²/m² = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²].
Answer: A

Q14. Which of the following is dimensionless?

A) Strain

B) Stress

C) Force

D) Energy

View Solution
Strain = change in length / original length. It is a ratio of two lengths, so it is dimensionless.
Answer: A

Q15. The dimensional formula of stress is:

A) [ML⁻¹T⁻²]

B) [MLT⁻²]

C) [ML²T⁻²]

D) [M⁰L⁰T⁰]

View Solution
Stress = Force / Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²].
Answer: A

Q16. The percentage error in measuring radius of a sphere is 2%. Percentage error in volume is:

A) 2%

B) 4%

C) 6%

D) 8%

View Solution
Volume of sphere V ∝ r³.

Percentage error in volume = 3 × 2% = 6%.
Answer: C

Q17. The smallest measurable value by an instrument is called:

A) Zero error

B) Least count

C) Accuracy

D) Precision

View Solution
Least count is the smallest value measurable by an instrument.
Answer: B

Q18. The SI unit of luminous intensity is:

A) Mole

B) Ampere

C) Candela

D) Kelvin

View Solution
The SI unit of luminous intensity is candela.
Answer: C

Q19. Which of the following is not a fundamental SI unit?

A) Kilogram

B) Kelvin

C) Newton

D) Ampere

View Solution
Newton is a derived unit of force. Kilogram, Kelvin and Ampere are fundamental SI units.
Answer: C

Q20. The dimensional formula of angular velocity is:

A) [T⁻¹]

B) [LT⁻¹]

C) [L²T⁻¹]

D) [M⁰L¹T⁻¹]

View Solution
Angular velocity = angle / time. Angle is dimensionless, so dimension = [T⁻¹].
Answer: A

Q21. The dimensional formula of torque is same as that of:

A) Power

B) Work

C) Pressure

D) Momentum

View Solution
Torque = Force × distance = [MLT⁻²][L] = [ML²T⁻²], same as work.
Answer: B

Q22. Which quantity has unit kg m² s⁻²?

A) Force

B) Energy

C) Power

D) Pressure

View Solution
kg m² s⁻² is Joule, the unit of energy.
Answer: B

Q23. If A = B + C, then dimensions of:

A) A, B and C may be different

B) B and C must be same, A may differ

C) A, B and C must be same

D) Only A and B must be same

View Solution
Only quantities with same dimensions can be added or subtracted. Hence A, B and C must have same dimensions.
Answer: C

Q24. The dimensional formula of frequency is:

A) [T]

B) [T⁻¹]

C) [LT⁻¹]

D) [MLT⁻¹]

View Solution
Frequency = 1 / Time period. Dimension = [T⁻¹].
Answer: B

Q25. The number 3.020 has how many significant figures?

A) 2

B) 3

C) 4

D) 5

View Solution
3.020 has four significant figures: 3, 0, 2, 0.
Answer: C

Q26. Which instrument is used to measure very small thickness accurately?

A) Metre scale

B) Spring balance

C) Screw gauge

D) Stop watch

View Solution
Screw gauge is used to measure very small thickness or diameter accurately.
Answer: C

Q27. If pitch of screw gauge is 1 mm and circular scale has 100 divisions, least count is:

A) 1 mm

B) 0.1 mm

C) 0.01 mm

D) 0.001 mm

View Solution
Least count = Pitch / Number of divisions = 1 mm / 100 = 0.01 mm.
Answer: C

Q28. The dimensional formula of surface tension is:

A) [MT⁻²]

B) [MLT⁻²]

C) [ML⁻¹T⁻²]

D) [M⁰LT⁻²]

View Solution
Surface tension = Force / Length = [MLT⁻²]/[L] = [MT⁻²].
Answer: A

Q29. Which of the following has dimensions of pressure?

A) Young’s modulus

B) Momentum

C) Power

D) Angular momentum

View Solution
Young’s modulus = Stress / Strain. Strain is dimensionless, so it has dimensions of stress or pressure.
Answer: A

Q30. The dimensional formula of coefficient of viscosity is:

A) [ML⁻¹T⁻¹]

B) [MLT⁻¹]

C) [ML⁻¹T⁻²]

D) [M⁰L⁰T⁰]

View Solution
Coefficient of viscosity η has unit Pa·s.

Pa = [ML⁻¹T⁻²], so η = [ML⁻¹T⁻¹].
Answer: A

Q31. In 2.5 × 10³, the number of significant figures is:

A) 1

B) 2

C) 3

D) 4

View Solution
Only 2 and 5 are significant. Power of ten does not affect significant figures.
Answer: B

Q32. Random errors can be reduced by:

A) Taking one reading only

B) Taking repeated readings and averaging

C) Using wrong zero correction

D) Avoiding calibration

View Solution
Random errors can be reduced by taking repeated readings and calculating their mean.
Answer: B

Q33. Zero error belongs to which type of error?

A) Random error

B) Systematic error

C) Gross error

D) Accidental error

View Solution
Zero error occurs due to faulty instrument setting. It is a systematic error.
Answer: B

Q34. Which of the following cannot be derived using dimensional analysis?

A) Checking correctness of equation

B) Finding relation between quantities

C) Finding numerical constant

D) Converting units

View Solution
Dimensional analysis cannot determine dimensionless numerical constants such as 2, π, 1/2.
Answer: C

Q35. The dimensional formula of Planck’s constant h is:

A) [ML²T⁻¹]

B) [ML²T⁻²]

C) [MLT⁻¹]

D) [M⁰L²T⁻¹]

View Solution
E = hν, so h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹].
Answer: A

Q36. Which of the following is dimensionally correct?

A) v = u + at

B) v = u + a/t

C) v = ut + a

D) v = u² + at

View Solution
In v = u + at, u and at both have dimensions of velocity [LT⁻¹].
Answer: A

Q37. If x = at + bt², dimensions of b are:

A) [LT⁻¹]

B) [LT⁻²]

C) [L²T⁻²]

D) [T⁻²]

View Solution
bt² has dimension of x, i.e. [L].

b = [L]/[T²] = [LT⁻²].
Answer: B

Q38. If y = A sin(ωt), dimensions of A are:

A) Same as y

B) Same as ω

C) Dimensionless

D) Same as time

View Solution
sin(ωt) is dimensionless, so A has same dimensions as y.
Answer: A

Q39. Which pair has the same dimensions?

A) Work and power

B) Torque and work

C) Pressure and force

D) Momentum and energy

View Solution
Torque and work both have dimensions [ML²T⁻²].
Answer: B

Q40. If measured value is 10.2 cm and true value is 10.0 cm, percentage error is:

A) 1%

B) 2%

C) 3%

D) 4%

View Solution
Error = 10.2 − 10.0 = 0.2 cm.

Percentage error = (0.2/10.0) × 100 = 2%.
Answer: B

Q41. Which quantity has dimensions [M⁰L⁰T⁰]?

A) Angle

B) Velocity

C) Acceleration

D) Force

View Solution
Angle is ratio of arc length to radius, so it is dimensionless.
Answer: A

Q42. The SI unit of amount of substance is:

A) Mole

B) Candela

C) Kelvin

D) Ampere

View Solution
The SI unit of amount of substance is mole.
Answer: A

Q43. The dimensional formula of electric charge is:

A) [AT]

B) [A/T]

C) [MLT⁻²]

D) [M⁰L⁰T⁰]

View Solution
Electric charge = Current × Time, so dimension = [AT].
Answer: A

Q44. The relative error is equal to:

A) Absolute error / True value

B) True value / Absolute error

C) Measured value × True value

D) Absolute error + True value

View Solution
Relative error = Absolute error / True value.
Answer: A

Q45. The unit of coefficient of friction is:

A) Newton

B) Joule

C) No unit

D) Pascal

View Solution
Coefficient of friction is ratio of frictional force to normal reaction, so it has no unit.
Answer: C

Q46. If momentum p = mv, dimensions of momentum are:

A) [MLT⁻¹]

B) [MLT⁻²]

C) [ML²T⁻²]

D) [M⁰LT⁻¹]

View Solution
Momentum = mass × velocity = [M][LT⁻¹] = [MLT⁻¹].
Answer: A

Q47. The dimensional formula of kinetic energy is:

A) [ML²T⁻²]

B) [MLT⁻²]

C) [ML²T⁻³]

D) [M⁰L²T⁻²]

View Solution
Kinetic energy = 1/2 mv² = [M][L²T⁻²] = [ML²T⁻²].
Answer: A

Q48. Which of the following represents precision?

A) Closeness to true value

B) Reproducibility of readings

C) Large error

D) Wrong calibration

View Solution
Precision means closeness of repeated readings to one another.
Answer: B

Q49. If a physical quantity Q = A²B/C, percentage error in Q is:

A) 2ΔA/A + ΔB/B + ΔC/C

B) ΔA/A + ΔB/B − ΔC/C

C) 2ΔA/A − ΔB/B + ΔC/C

D) ΔA/A + 2ΔB/B + ΔC/C

View Solution
For Q = A²B/C, relative error = 2(ΔA/A) + (ΔB/B) + (ΔC/C).
Answer: A

Q50. The dimensional formula of acceleration due to gravity g is:

A) [LT⁻¹]

B) [LT⁻²]

C) [MLT⁻²]

D) [M⁰L⁰T⁻¹]

View Solution
Acceleration due to gravity is acceleration. Dimension = [LT⁻²].
Answer: B
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