JEE Physics Quiz for Unit Dimension MCQ

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

1. length, mass and velocity
2. length, time and velocity
3. mass, time and velocity
4. length, time and mass

A dimensionless quantity

1. never has a unit
2. always has a unit
3. may have a unit
4. does not exit

A unit less quantity

1. never has a nonzero dimension
2. always has a nonzero dimension
3. may have a nonzero dimension
4. 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)

1. v² =kλ^-1 g^-1 λ^-1
2. v² =kgλ
3. v² =kgλρ
4. v² =kλ³ g^-1 ρ^-1

The value of G = 6.67 × 10^-11 N m² (kg)^-2 . Its numerical value in CGS system will be :

1. 6.67 × 10^-8
2. 6.67 × 10^-6
3. 6.67
4. 6.67 × 10^-5

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

1. ρAv
2. ρAv²
3. ρ²Av
4. ρA2v

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

1. doubled
2. halved
3. four times
4. 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

1. MLT^–2, M⁰L⁰T^-1
2. MLT^–2, M⁰L^–1T⁰
3. M⁰L⁰T⁰, M⁰L¹T^-1
4. M⁰L¹T^-1, M⁰L⁰T⁰

Choose the correct statement(s):

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

Choose the correct statement(s) :

1. A dimensionally correct equation may be correct.
2. A dimensionally correct equation may be incorrect.
3. A dimensionally incorrect equation may be correct.
4. A dimensionally incorrect equation must be incorrect.

The dimensions of a are the same as those of

1. PV
2. PV²
3. P²V
4. P/V

The dimensions of b are the same as those of

1. P
2. V
3. PV
4. nRT

The dimensional formula for ab is

1. ML²T^-2
2. ML⁴T^-2
3. ML⁶T^-2
4. ML⁸T^-2