Question:
A quantity $x$ is given by $(IFv^2 / WL^{4})$ in terms of moment of inertia $I, $ force $ F$, velocity $v ,$ work $W$ and Length $L$. The dimensional formula for $x$ is same as that of :
A quantity $x$ is given by $(IFv^2 / WL^{4})$ in terms of moment of inertia $I, $ force $ F$, velocity $v ,$ work $W$ and Length $L$. The dimensional formula for $x$ is same as that of :
Updated On: Jul 13, 2024
- Planck's constant
- Force constant
- Energy density
- Coefficient of viscosity
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$x =\frac{ IFV ^{2}}{ WL ^{4}}$
$[ x ]=\frac{\left[ ML ^{2}\right]\left[ MLT ^{-2}\right]\left[ LT ^{-1}\right]^{2}}{\left[ ML ^{2} T ^{-2}\right][ L ]^{4}}$
$[ x ]=\left[ ML ^{-1} T ^{-2}\right]$
[Energy density] $=\left[\frac{ E }{ V }\right]$
$=\left[\frac{ ML ^{2} T ^{-2}}{ L ^{3}}\right]$
$=\left[ ML ^{-1} T ^{-2}\right]$
Same as $x$
$[ x ]=\frac{\left[ ML ^{2}\right]\left[ MLT ^{-2}\right]\left[ LT ^{-1}\right]^{2}}{\left[ ML ^{2} T ^{-2}\right][ L ]^{4}}$
$[ x ]=\left[ ML ^{-1} T ^{-2}\right]$
[Energy density] $=\left[\frac{ E }{ V }\right]$
$=\left[\frac{ ML ^{2} T ^{-2}}{ L ^{3}}\right]$
$=\left[ ML ^{-1} T ^{-2}\right]$
Same as $x$
Was this answer helpful?
0
0
Top Questions on physical world
- Evaluate the integral: ∫ log((2 + x)2 + x) dx
- MHT CET - 2025
- Physics
- physical world
- If y = tan-1 ((2 + 3x) / (3 - 2x)) + tan-1 (4x / (1 + 5x2)), thendy/dx =
- MHT CET - 2025
- Physics
- physical world
- The area enclosed between the parabola \( y^2 = 4x \) and the line \( y = 2x - 4 \) is:
- MHT CET - 2025
- Physics
- physical world
- The particular solution of the differential equation, \[ x y \frac{dy}{dx} = x^2 + 2y^2 \quad \text{when} \quad y(1) = 0 \quad \text{is:} \]
- MHT CET - 2025
- Physics
- physical world
- For all real x, the minimum value of the function f(x) = (1 - x + x^2) / (1 + x + x^2) is:
- MHT CET - 2025
- Physics
- physical world
View More Questions
Questions Asked in JEE Main exam
- Number of solutions in the interval \( [-2\pi, 2\pi] \) for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]
- JEE Main - 2025
- Trigonometry
- The spin-only magnetic moment (\(\mu\)) value (B.M.) of the compound with the strongest oxidising power among \(Mn_2O_3\), \(TiO\), and \(VO\) is ________________________ B.M. (Nearest integer).
- JEE Main - 2025
- Magnetic moment
- Atomic number of element with lowest first ionisation enthalpy is:
- JEE Main - 2025
- Periodic Table
- Let \( z_1, z_2, z_3 \) be three complex numbers on the circle \( |z| = 1 \) with \( \arg(z_1) = -\frac{\pi}{4}, \arg(z_2) = 0 \) and \( \arg(z_3) = \frac{\pi}{4} \). If \( |z_1 \overline{z_2} + z_2 \overline{z_3} + z_3 \overline{z_1}|^2 = \alpha + \beta \sqrt{2} \), where \( \alpha, \beta \in \mathbb{Z} \), then the value of \( \alpha^2 + \beta^2 \) is :
- JEE Main - 2025
- complex numbers
- The kinetic energy of translation of the molecules in 50 g of CO\(_2\) gas at 17°C is:
- JEE Main - 2025
- The Kinetic Theory of Gases
View More Questions
Concepts Used:
Physical World
The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:
- Gravitational Force is a universal force that exists as an outcome of mutual attraction between any two objects with respect to their masses.
- Electromagnetic Force can be understood as the force that is present between the charged particles. The force is stated by Coulomb’s law.
- Strong Nuclear Force is the force that ties the protons and neutrons in a nucleus. Of all the elemental forces in nature, a strong nuclear force is the strongest as its name suggests.
- Weak Nuclear Force can only be noticed in some of the nuclear processes such as the beta decay of the nucleus.