Match List-I with List-II.
Match List-I with List-II.
Show Hint
(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
(A)-(II), (B)-(I), (C)-(III), (D)-(IV)
(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
The Correct Option is D
Solution and Explanation
- Magnetic field \( B \) has the dimensional formula \( [M T^{-2} A^{-1}] \).
- Magnetic moment \( M \) has the dimensional formula \( [M L T^{-2} A^{-2}] \).
- Torsional constant has the dimensional formula \( [L^2 A] \). Thus, the correct matching is: \[ % Option (A)-(III), (B)-(II), (C)-(IV), (D)-(I). \]
Top Questions on Dimensional analysis
Match List-I with List-II.
List-I
(A) Coefficient of viscosity
(B) Intensity of wave
(C) Pressure gradient
(D) CompressibilityList-II
(I) [ML-1T-1]
(II) [MT-3]
(III) [ML-2T-2]
(IV) [M-1LT2]- JEE Main - 2025
- Physics
- Dimensional analysis
The equation for real gas is given by $ \left( P + \frac{a}{V^2} \right)(V - b) = RT $, where $ P $, $ V $, $ T $, and $ R $ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ ab $ is equivalent to that of:
- JEE Main - 2025
- Physics
- Dimensional analysis
- The shape of an elastic rod of length \( l \) is represented by the position vector \( \vec{r}(s) \) corresponding to the arc length \( s \). If the bending energy of the rod is \[ E = K \int_0^l \left( \frac{\partial^2 \vec{r}}{\partial s^2} \right)^2 \, ds, \] what is the dimension of \( K \) in terms of mass \( M \), length \( L \), and time \( T \)?
- GATE BM - 2025
- Biomechanics
- Dimensional analysis
The dimensions of a physical quantity \( \epsilon_0 \frac{d\Phi_E}{dt} \) are similar to [Symbols have their usual meanings]
- JEE Main - 2025
- Physics
- Dimensional analysis
- The dimensions of a physical quantity \( \epsilon_0 \frac{d\Phi_E}{dt} \) are similar to:
- JEE Main - 2025
- Physics
- Dimensional analysis
Questions Asked in JEE Main exam
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- complex numbers
- If for some \( \alpha, \beta \); \( \alpha \leq \beta \), \( \alpha + \beta = 8 \) and \[ \sec^2(\tan^{-1} \alpha) + \csc^2(\cot^{-1} \beta) = 36, \] then \( \alpha^2 + \beta \) is:
- JEE Main - 2025
- Quadratic Equations
Match List - I with List - II:
List - I:
(A) Electric field inside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
(B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet with surface charge density \( \sigma \).
(C) Electric field outside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density \( \sigma \).List - II:
(I) \( \frac{\sigma}{\epsilon_0} \)
(II) \( \frac{\sigma}{2\epsilon_0} \)
(III) 0
(IV) \( \frac{\sigma}{\epsilon_0 r^2} \) Choose the correct answer from the options given below:- JEE Main - 2025
- Electrostatics
Consider the following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases.
D. The onset of turbulence is determined by Reynolds number.
E. In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:- JEE Main - 2025
- Fluid Mechanics
- A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.
- JEE Main - 2025
- Fluid Mechanics