Dimension of \(\frac{1}{μ_0∈_0}\) should be equal to
- \(\frac{L}{T}\)
- \(\frac{T}{L}\)
- \(\frac{L^2}{T^2}\)
- \(\frac{T^2}{L^2}\)
The Correct Option is C
Solution and Explanation
Step 1: Use the relationship between µ0, ϵ0, and the speed of light.- Given $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$, we know:
$\frac{1}{\mu_0 \epsilon_0} = c^2$.
Step 2: Analyze the dimensions.- Dimensional formula for c: [c] = $\frac{L}{T}$.- Hence, $[\frac{1}{\mu_0 \epsilon_0}]$ = $[c^2]$ = $\frac{L^2}{T^2}$.
Final Answer: The dimension is $\frac{L^2}{T^2}$
Top Questions on work, energy and power
- Given below are two statements:
Statement I: An object moves from position \( \vec{r}_1 \) to position \( \vec{r}_2 \) under a conservative force field \( \vec{F} \). The work done by the force is \[ W = -\int_{\vec{r}_1}^{\vec{r}_2} \vec{F} \cdot d\vec{r}. \]
Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2026
- Physics
- work, energy and power
- Two masses \(m\) and \(2m\) are connected by a light string going over a pulley (disc) of mass \(30m\) with radius \(r=0.1\,\text{m}\). The pulley is mounted in a vertical plane and is free to rotate about its axis. The \(2m\) mass is released from rest and its speed when it has descended through a height of \(3.6\,\text{m}\) is ____________ m/s. (Assume string does not slip and \(g=10\,\text{m s}^{-2}\)).
- JEE Main - 2026
- Physics
- work, energy and power
- A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass $M$ remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass $M$ as $\mu$, is :
- JEE Main - 2026
- Physics
- work, energy and power
Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.
- JEE Main - 2026
- Physics
- work, energy and power
- A body of mass 4 kg is placed on a plane at a point P having coordinate $(3,4)$ m. Under the action of force $\vec{F} = (2\hat{i} + 3\hat{j})$ N, it moves to a new point Q having coordinates $(6,10)$ m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:
- JEE Main - 2026
- Physics
- work, energy and power
Questions Asked in JEE Main exam
- For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).
- JEE Main - 2026
- Current electricity
- For three unit vectors \( \vec a, \vec b, \vec c \) satisfying \[ |\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9 \] and \[ |2\vec a + k\vec b + k\vec c| = 3, \] the positive value of \( k \) is:
- JEE Main - 2026
- Vector Algebra
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements