Quiz on Ch - 1(Units & Measurements)

The pair of quantities having the same dimensions is

• wavelength, focal length

• time, frequency

• displacement, velocity

• force, acceleration

Answer explanation

The pair of quantities with the same dimensions is wavelength and focal length, as they both have units of length (meters).

Average distance of the Sun from the Earth is measured in

• light year

• astronomical unit

• parsec

• fermi

Answer explanation

The average distance of the Sun from the Earth is measured in astronomical units, which is the correct choice among the options provided.

The number of significant figures in the number 0.0028 is

• 5

• 3

• 2

• 4

Answer explanation

The number 0.0028 has 2 significant figures, which are the non-zero digits 2 and 8. Zeros before the first non-zero digit are not significant.

Which of the following is not the unit of time

• light year

• second

• minute

• month

Answer explanation

The correct choice is 'light year' because it is a unit of distance, not time like the other options (second, minute, month).

If x = a + bt + ct^2, where x is in metre and t in second, then what is the unit of ‘c’?

• m/s

• m/s^2

• m^2/s

• kgm/s

Answer explanation

The unit of 'c' can be determined by analyzing the given equation. As c is multiplied by t^2, the unit of c is m/s^2.

The base quantity among the following is

• area

• length

• weight

• Speed

Answer explanation

The base quantity among the following is 'length' because it is a fundamental measurement from which other quantities like area, weight, and speed are derived.

Dimensional analysis can be applied to

• to check the correctness of a physical equation

• to derive the relationship between different physical quantities

• to convert a physical quantity from one system of units to other

• All of the above

Answer explanation

Dimensional analysis can be applied to check the correctness of a physical equation, derive the relationship between different physical quantities, and convert a physical quantity from one system of units to another, making 'All of the above' the correct choice.

Which of the following physical quantity has the dimensional formula [M^1L^2T^-3]

• impulse

• power

• work

• work

Answer explanation

The physical quantity with the dimensional formula [M^1L^2T^-3] is power, as it is the only option that matches the given dimensions.

The dimensions of universal gravitational constant is

• [M^-1L^3T^-2]

• [M^1L^1T^-2]

• [M^-1L^2T^-2]

• [M^1L^-1T^-1]

Answer explanation

The correct dimensions of universal gravitational constant are [M^-1L^3T^-2], as it represents mass to the power of -1, length to the power of 3, and time to the power of -2.

Which of the following is dimensionless

• velocity/acceleration

• energy/work

• force/acceleration

• volume/area

Answer explanation

Energy/work is dimensionless because both have the same units (joules) and can be expressed as a ratio, resulting in a dimensionless quantity.