Units & Dimensions

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Q1. Which of the following is the correct dimensional formula for acceleration? (2022)

Solution:

Acceleration is defined as the change in velocity per unit time, so its dimensional formula is [M^0 L^1 T^-2].

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Q2. Which of the following quantities has no dimensions? (2019)

Solution:

Angle is a pure number and has no dimensions, while force, energy, and pressure all have dimensions.

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Q3. If the speed of light is 3 x 10^8 m/s, what is its value in km/s? (2021)

Solution:

To convert m/s to km/s, divide by 1000. Therefore, 3 x 10^8 m/s = 3 x 10^5 km/s.

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Q4. The unit of energy in the SI system is equivalent to which of the following? (2020)

Solution:

Energy is measured in Joules, and 1 Joule is defined as 1 Newton-meter, hence both A and B are correct.

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Q5. Which of the following is the correct dimensional formula for energy? (2023)

Solution:

Energy has the dimensional formula [M^1 L^2 T^-2], as it is defined as work done, which is force times distance.

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Q6. The dimensional formula for frequency is: (2023)

Solution:

Frequency is defined as the number of cycles per unit time, hence its dimensional formula is [T^-1].

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Q7. Which of the following is a base quantity? (2020)

Solution:

Length is a base quantity in the SI system, while force, energy, and pressure are derived quantities.

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Q8. The unit of electric charge in the SI system is: (2022)

Solution:

Coulomb (C) is the SI unit of electric charge.

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Q9. If a physical quantity has dimensions [M^0 L^1 T^-1], what is it? (2020)

Solution:

The dimensions [M^0 L^1 T^-1] correspond to velocity, which is defined as distance traveled per unit time.

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Q10. Which of the following is a base unit in the SI system? (2020)

Solution:

Meter is a base unit in the SI system, while liter, newton, and joule are derived units.