Practice Questions - Units & Dimensions (JEE Advanced) - MCQ

Which of the following is not the unit of energy?

If the unit of length is micrometer and the unit of time is microsecond, the unit of velcoity will be :

A dimensionless quantity :

A unitless quantity :

If a and b are two physical quantities having different dimensions then which of the following can denote a new physical quantity

Two physical quantities whose dimensions are not same, cannot be :

Choose the correct statement(s) :

Planck's constant has the dimensions of :

The velocity 'v' (in cm/s) of a particle is given in terms of time 't' (in s) by the equation   . The dimensions of a, b and c are

The position of a particle at time 't' is given by the relation  . where V₀ is a constant and α > 0. The dimensions of V₀ and α are respectively.

The time dependence of a physical quantity ?   P = P₀exp(–αt²).  where α is a constant and t is time .The constant α

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

The Van der Waal equation for 1 mole of a real gas is   .where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are Van dar Waal constants. The dimensions of a are the same as those of

The Van der Waal equation for 1 mole of a real gas is  .where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are Van dar Waal constants. the dimensions of b are the same as those of

The Van der Waal equation for 1 mole of a real gas is  .where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are Van dar Waal constants.the dimensions of nRT are the same as those of

The Van der Waal equation for 1 mole of a real gas is  .where P is the pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are Van dar Waal constants.the dimensional formula for ab is

Which pair of following quantities has dimensions different from each other.

If force (F) is given by F = Pt^-1 + αt,where t is time. The unit of P is same as that of

The product of energy and time is called action. The dimensional formula for action is same as that for

When a wave traverses a medium, the displacement of a particle located at x at time t is given by y = a sin (bt – cx). where a, b and c are constants of the wave. The dimensions of b are the same as those of

When a wave traverses a medium, the displacement of a particle located at x at time t is given by y = a sin (bt – cx). where a, b and c are constants of the wave.The dimensions of b/c are the same as those of

What is the physical quantity whose dimensions are M L² T^-2 ?

If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be :

The dimensions ML^-1T^-2 can correspond to

Which of the following can be a set of fundamental quantities

If area (A) velocity (v) and density (ρ) are base units, then the dimensional formula of force can be represented as

In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and unit of length is 10m. In this system, one unit of power will correspond to