Question:
If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young's modulus will be :
If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young's modulus will be :
Updated On: Jun 29, 2024
- $V^{-2} A^2 F^2$
- $V^{-4} A^2 F$
- $V^{-4} A^{-2} F$
- $V^{-2} A^2 F^{-2}$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$\frac{F}{A} = y . \frac{\Delta\ell}{\ell} $
$ \left[Y\right] = \frac{F}{A}$
$ F = \frac{ML}{T^{2}} $
$ L = \frac{F}{M} .T^{2} $
$ L^{2} = \frac{F^{2}}{M^{2}} \left(\frac{V}{A}\right)^{4} \because T = \frac{V}{A}$
$ L^{2} = \frac{F^{2}}{M^{2}A^{2}} \frac{v^{4}}{A^{2}} F = MA $
$ L^{2} = \frac{V^{2}}{A^{2}} $
$ \left[Y\right] = \frac{\left[F\right]}{\left[A\right]} = F^{1} V^{-4} A^{2} $
$ \left[Y\right] = \frac{F}{A}$
$ F = \frac{ML}{T^{2}} $
$ L = \frac{F}{M} .T^{2} $
$ L^{2} = \frac{F^{2}}{M^{2}} \left(\frac{V}{A}\right)^{4} \because T = \frac{V}{A}$
$ L^{2} = \frac{F^{2}}{M^{2}A^{2}} \frac{v^{4}}{A^{2}} F = MA $
$ L^{2} = \frac{V^{2}}{A^{2}} $
$ \left[Y\right] = \frac{\left[F\right]}{\left[A\right]} = F^{1} V^{-4} A^{2} $
Was this answer helpful?
0
0
Top Questions on 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
- Evaluate the integral: ∫ log((2 + x)2 + x) dx
- 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
- 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
- Assume a living cell with 0.9%(\(w/w\)) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:
- JEE Main - 2025
- osmosis
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.