The equation of state of a real gas is given by where and are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of is similar to that of: [2024]
(2)
And
Match List-I with List-II [2024]
List-I | List-II | ||
A. | Coefficient of viscosity | I. | |
B. | Surface tension | II. | |
C. | Angular momentum | III. | |
D. | Rotational kinetic energy | IV. |
A-II, B-I, C-IV, D-III
A-I, B-II, C-III, D-IV
A-III, B-IV, C-II, D-I
A-IV, B-III, C-II, D-I
(3)
(A) Coefficient of viscosity
(B) Surface Tension
(C) Angular momentum
(D) Rotational Kinetic Energy
If mass is written as then the value of will be (Constants have their usual meaning with a dimensionless constant) [2024]
1/2
1/3
2
- 1/3
(1)
...(1)
Now using (1)
Compare the dimension of T from L.H.S and R.H.S then
A force is represented by where = distance and = time. The dimensions of are [2024]
(2)
Consider two physical quantities A and B related to each other as where and have dimensions of energy, length and time respectively. The dimension of A B is [2024]
(2)
The dimensional formula of angular impulse is [2024]
(4)
Angular impulse = change in angular momentum.
[Angular impulse] = [Angular momentum] = []
=
If B is magnetic field and is permeability of free space, then the dimensions of () is [2025]
(2)
Magnetic field at the axis of a long solenoid,
Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T and C stand for unit of mass, length, time and charge, [2025]
(4)
The position of a particle moving on x-axis is given by x(t) = A sin t + B + + D, where t is time. The dimension of is [2025]
L
(3)
Dimension [x(t)] = [L]
[A] = [L]
[B] = [L]
[C] = []
[D] = [L]
The electric flux is , where and are linear and surface charge density, respectively, represents [2025]
charge
electric field
displacement
area
(3)