MCQs on Units and Dimensions (With Solutions)-Part I

 

 

Q1. Which of the following pairs have the same dimensions?

A. Energy and Torque
B. Power and Force
C. Momentum and Impulse
D. Pressure and Stress

Answer: C. Momentum and Impulse

Solution:

• Momentum = mv = [M][L] [T⁻¹]
• Impulse = F⋅t= [M][L] [T⁻¹]
  Hence, same dimensions.

Q2. Which of the following quantities is dimensionally different from the others?

A. Work
B. Energy
C. Torque
D. Power

Answer: D. Power

Solution:

• Work, Energy, Torque: [ML²T⁻²]
• Power = [ML²T⁻³] → Different

Q3. The dimensional formula for Planck's constant is:

A. [ML²T⁻¹]
B. [MLT⁻²]
C. [ML²T⁻²]
D. [ML²T⁻³]

Answer: A. [ML²T⁻¹]

Solution:
E=hν⇒h=E/ν
h=[ML²T⁻²]/[T⁻¹] =[ML²T⁻¹]

 

Q4. Which physical quantity has the same dimensions as that of pressure?

A. Energy
B. Force
C. Stress
D. Torque

Answer: C. Stress

Solution:
Both Pressure and Stress = [ML⁻¹T⁻²]

Q5. If the acceleration a is given by a=v² /r​, the dimensions of r are:

A. [L]
B. [LT²]
C. [T²]
D. [L²T⁻¹]

Answer: A. [L]

Solution:
[a]=[LT⁻²] =[v]² /[r]=[L²T⁻²]/[r]⇒[r]=[L]

Q6. The dimension of gravitational constant G is:

A. [M⁻¹L³T⁻²]
B. [ML³T⁻²]
C. [M⁻¹L²T²]
D. [M²L²T⁻⁴]

Answer: A. [M⁻¹L³T⁻²]

Solution:
From F=Gm₁m_{2 /}r^2​​,
G=Fr² /m²=[MLT⁻²] L² /M²=[M⁻¹L³T⁻²]

Q7. A velocity v= at + bt². What are the dimensions of b?

A. [LT⁻²]
B. [LT⁻³]
C. [L²T⁻²]
D. [L²T⁻³]

Answer: B. [LT⁻³]

Solution:
Both terms in the equation must have dimensions of velocity [LT⁻¹]

• bt²⇒b=[LT⁻¹]/[T²] =[LT⁻³]

Q8. Which quantity is dimensionless?

A. Strain
B. Force constant
C. Frequency
D. Angle in radians

Answer: A. Strain

Solution:
Strain = Change in length / Original length = Dimensionless

Q9. Which of the following is not correctly matched?

A. Pressure → [ML⁻¹T⁻²]
B. Power → [ML²T⁻³]
C. Work → [ML²T⁻²]
D. Energy → [MLT⁻²]

Answer: D. Energy → [MLT⁻²] ❌

Solution:
Correct dimensions of Energy = [ML²T⁻²]

Q10. Which of the following combinations has dimensions of velocity?

A. Force/Mass
B. Distance/Time²
C. Work/(Force⋅Time)
D. Acceleration/Time

Answer: C. Work/(Force⋅Time)

Solution:

• Work = Force × Distance
• So, Work / (Force × Time) = Distance / Time = Velocity

Q11. If kinetic energy KE=1/2mv², its dimensions are:

A. [MLT⁻²]
B. [ML²T⁻²]
C. [ML²T⁻³]
D. [ML²T⁻¹]

Answer: B. [ML²T⁻²]

Solution:
KE=1/2mv²=[M][L²T⁻²]

Q12. Which quantity has the same dimension as angular momentum?

A. Work
B. Energy
C. Planck’s constant
D. Force

Answer: C. Planck’s constant

Solution:
Both Angular Momentum and Planck's constant = [ML²T⁻¹]

Q13. What is the dimensional formula of surface tension?

A. [MT⁻²]
B. [MLT⁻³]
C. [MT⁻¹]
D. [ML⁰T⁻²]

Answer: A. [MT⁻²]

Solution:
Surface Tension = Force / Length = [MLT⁻²]/[L]=[MT⁻²]

Q14. The unit of impulse is:

A. Joule
B. Newton-second
C. Watt
D. kg m²/s

Answer: B. Newton-second

Solution:
Impulse = Force × Time = N·s

Q15. Which is dimensionally correct?

A. Speed = Distance × Time
B. Work = Force × Acceleration
C. Energy = Power × Time
D. Force = Mass / Time

Answer: C. Energy = Power × Time

Solution:

• Power = Energy/Time ⇒ Energy = Power × Time ✅

Q16. Which has dimensions of pressure?

A. Force/Area
B. Energy/Volume
C. Stress
D. All of the above

Answer: D. All of the above

Solution:
Each of these has dimensions: [ML⁻¹T⁻²]

Q17. The unit of dimensional constant in the equation v=u+at is:

A. m/s
B. m/s²
C. s
D. dimensionless

Answer: B. m/s²

Solution:
The constant a (acceleration) has units: m/s²

Q18. Which is a derived quantity?

A. Mass
B. Temperature
C. Time
D. Work

Answer: D. Work

Solution:
Work is derived from force and displacement ⇒ Derived quantity.

Q19. The dimensional formula of power is:

A. [MLT⁻³]
B. [ML²T⁻³]
C. [ML²T⁻²]
D. [ML²T⁻¹]

Answer: B. [ML²T⁻³]

Solution:
Power = Energy / Time = [ML²T⁻²]/[T]=[ML²T⁻³]

Q20. The value of g on a planet is calculated using g=4π²LT²​. What is the unit of g?

A. m/s
B. m/s²
C. m²/s
D. m²/s²

Answer: B. m/s²

Solution:
g=L/T²⇒[LT⁻²]

Q21. A quantity has unit Js (joule-second). It could be:

A. Energy
B. Torque
C. Planck’s constant
D. Impulse

Answer: C. Planck’s constant

Solution:
Planck’s constant has unit of energy × time = Joule·second

Q22. Which one is dimensionless but not unitless?

A. Refractive Index
B. Angle in radians
C. Strain
D. Coefficient of friction

Answer: B. Angle in radians

Solution:
Radians = arc/radius (dimensionless) but has unit “radian”

Q23. Choose the correct match of quantity and unit:

A. Force — joule
B. Energy — newton
C. Power — watt
D. Work — pascal

Answer: C. Power — watt

Solution:
Force = newton
Energy = joule
Power = watt
Work = joule

Q24. Which quantity has same dimension as work?

A. Torque
B. Heat
C. Energy
D. All of these

Answer: D. All of these

Solution:
All have dimensions: [ML²T⁻²]

Q25. If force F=ma, dimensions of F are:

A. [MLT⁻¹]
B. [ML²T⁻¹]
C. [MLT⁻²]
D. [ML²T⁻²]

Answer: C. [MLT⁻²]

Solution:
F = m × a → [M][LT⁻²] =[MLT⁻²]