The dimensional formula for relative density is
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(d) Relative density
Hence no dimension.
The dimensions of speed and velocity are
(d) Speed and velocity
The division of energy by time is . The dimensional formula of is same as that of
momentum
torque
power
electric field
(b) Power
The dimensions of energy density of magnetic field , where is magnetic field and is the magnetic permeability of vacuum, is
(d) Energy density of magnetic field,
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be
(a) Pascal second
Identify the pair of physical quantities which have different dimensions :
Wave number and Rydberg's constant
Stress and Coefficient of elasticity
Coercivity and Magnetisation
Specific heat capacity and Latent heat
(d) Waye number and Rydberg constant have same unit .
Stress and coefficient of elasticity have same unit Pascal (P).
Coercivity and magnetisation have same unit .
Whereas, specific heat capacity, has unit
and latent heat, has unit .
If the dimensions of a physical quantity are given by , then the physical quantity will be
velocity if
acceleration if
force if
pressure if
(d) Pressure
Which of the following physical quantities have the same dimensions?
Electric displacement and surface charge density
Displacement current and electric field
Current density and surface charge density
Electric potential and energy
(a) As current and electric field have different units. So options (b) is incorrect. As current density and surface charge density . So both have different unit.
As electric potential and energy has unit of ' '.
So both have different unit. Now, only option left is (A), which must be correct
Also,
A quantity is given by where is the permittivity of the free space, is a length, is a potential difference and is a time interval. The dimensional formula for is the same as that of
resistance
charge
voltage
current
(d) Dimensionally where capacitance Now the given expression reduces to . Dimensionally where is charge.
Again the given expression reduces to .
Dimensionally where is current
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