Identify the pair of physical quantities that have same dimensions :
- velocity gradient and decay constant
- wien’s constant and Stefan constant
- angular frequency and angular momentum
- wave number and Avogadro number
The Correct Option is A
Solution and Explanation
Velocity gradient
= \(\frac{dv}{dx}\)
⇒ Dimensions are
\(\frac{[LT-1]}{[L]}=[T-1]\)
Decay constant \(λ\) has dimensions of \([T^{–1}]\) because of the relation
\(\frac{dN}{dt} = -λN\)
⇒ Velocity gradient and decay constant have same dimensions.
Top Questions on Speed and velocity
- Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:
- JEE Main - 2025
- Physics
- Speed and velocity
- A fluid flows through a pipe with varying cross-section. If the velocity at the narrow section is 3 m/s and the cross-sectional area is half of the wider section, what is the velocity in the wider section?
- BITSAT - 2025
- Physics
- Speed and velocity
- A ball of mass \(120\) \(g\) moving with initial velocity \(25 \;m/s\) is stopped by an external force \(F\) in \(0.15\) \(sec\). Find value of \(F\) in newton :
- JEE Main - 2024
- Physics
- Speed and velocity
- Two trains run on North-South parallel tracks. Train A moves with velocity 20 m/s towards North and train B moves with velocity 30 m/s towards South. Then find the velocity of train B with respect to train A
- JEE Main - 2024
- Physics
- Speed and velocity
- A uniform disk of mass \(50\) \(kg\) is rolling without slipping with a speed of \(0.4 \;m/s\). Find minimum energy required to bring the disk to rest (in \(J\)).
- JEE Main - 2024
- Physics
- Speed and velocity
Questions Asked in JEE Main exam
- Evaluate: \[ \frac{6}{3^{26}}+\frac{10\cdot1}{3^{25}}+\frac{10\cdot2}{3^{24}}+\frac{10\cdot2^{2}}{3^{23}}+\cdots+\frac{10\cdot2^{24}}{3}. \]
- JEE Main - 2026
- Integral Calculus
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
- If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to
- JEE Main - 2026
- Binomial theorem
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\).
- JEE Main - 2026
- Current electricity
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
Concepts Used:
Speed and Velocity
The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.
Difference Between Speed and Velocity:
Read More: Difference Between Speed and Velocity