name any two physical quantity which have same dimension can a quantity have a unit but no dimension explain it
Answers
Answer:
pressure ,stress have the same dimension i.e. M1L-1T-2
yes a quantity have unit but no dimension.
✍️ Length, breadth, height, depth, thickness, diameter, radius, perimeter, distance, displacement all have same dimensions.
✍️ Frequency, Circular frequency, angular velocity, velocity gradient all have same dimensions.
✍️ Work, energy, torque have same dimensions.
✍️ Pressure, stress, Young's modulus, bulk modulus, rigidity modulus have same dimensions.
✍️ Momentum and impulse of force have same dimensions.
✍️ Force and weight have same dimensions.
✍️ Angular momentum and Planck's constant have same dimensions.
✍️ Yes, a quantity can have a unit but no dimension. For example, angle. Consider an angle, theta subtended by a circular arc at the centre of a circle.
Then, Angle theta = length of the circular arc ÷ Radius of the circle = L ÷ L = 1
The dimension of angle theta is equal to 1 indicates that angle theta is a dimensionless quantity.
✔️ ANOTHER EXAMPLE :
✍️ Solid angle is also an example of a physical quantity which have unit but no dimension. The dimension of solid angle is 1 which indicates that solid angle is dimensionless but still solid angle has a unit of STERIDIAN.