**JEE Physics Quiz for Unit Dimension MCQ:** Dimensions are physical quantities that can be measured, whereas units are arbitrary names that correlate to particular dimensions to make them relative.

## Table of Contents

**Unit Dimension MCQ**

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

- length, mass and velocity
- length, time and velocity
- mass, time and velocity
- length, time and mass

A dimensionless quantity

- never has a unit
- always has a unit
- may have a unit
- does not exit

A unit less quantity

- never has a nonzero dimension
- always has a nonzero dimension
- may have a nonzero dimension
- does not exit

The velocity of water waves may depend on their wavelength λ the density of water ρ acceleration due to gravity g. The method of dimensions gives the relation between these quantities as: (where k is a dimensionless constant)

- v
^{2}=kλ^{-1}g^{-1}λ^{-1} - v
^{2}=kgλ - v
^{2}=kgλρ - v
^{2}=kλ^{3}g^{-1}ρ^{-1}

^{2}=kgλ

The value of G = 6.67 × 10^{-11} N m^{2} (kg)^{-2} . Its numerical value in CGS system will be :

- 6.67 × 10
^{-8} - 6.67 × 10
^{-6} - 6.67
- 6.67 × 10
^{-5}

^{-8}

Force applied by water stream depends on density of water (ρ), velocity of the stream (v) and cross – sectional area of the stream (A). The expression of the force should be

- ρAv
- ρAv
^{2} - ρ
^{2}Av - ρA2v

^{2}

If unit of length and time is doubled, the numerical value of ‘g’ (acceleration due to gravity) will be :

- doubled
- halved
- four times
- remain same

Force F is given in terms of time t and distance x by

F = A sin C t + B cos D x

Then the dimensions of A/B and C/D are given by

- MLT
^{–2}, M^{0}L^{0}T^{-1} - MLT
^{–2}, M^{0}L^{–1}T^{0} - M
^{0}L^{0}T^{0}, M^{0}L^{1}T^{-1} - M
^{0}L^{1}T^{-1}, M^{0}L^{0}T^{0}

^{0}L

^{0}T

^{0}, M

^{0}L

^{1}T

^{-1}

Choose the correct statement(s):

- All quantities may be represented dimensionally in terms of the base quantities.
- A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
- The dimension of a base quantity in other base quantities is always zero.
- The dimension of a derived quantity is never zero in any base quantity.

Choose the correct statement(s) :

- A dimensionally correct equation may be correct.
- A dimensionally correct equation may be incorrect.
- A dimensionally incorrect equation may be correct.
- A dimensionally incorrect equation must be incorrect.

The dimensions of a are the same as those of

- PV
- PV
^{2} - P
^{2}V - P/V

^{2}

The dimensions of b are the same as those of

- P
- V
- PV
- nRT

The dimensional formula for ab is

- ML
^{2}T^{-2} - ML
^{4}T^{-2} - ML
^{6}T^{-2} - ML
^{8}T^{-2}

^{8}T

^{-2}