The dimensional formula of torque is
- $[ML^2T^{-2}]$
- $[MLT^{-2}]$
- $[ML^{-1}T^{-2}]$
- $[ML^{-2}T^{-2}]$
The Correct Option is A
Solution and Explanation
Dimensional formula for $(\tau)=[MLT^{-2}][L]$
$ =[ML^2T^{-2}]$
Top Questions on Dimensional Analysis
- Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.
- JEE Main - 2025
- Physics
- Dimensional Analysis
- In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of \( [M^a L^b T^c] \). If \( b = 3 \), the value of \( c \) is:
- JEE Main - 2025
- Physics
- Dimensional Analysis
The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = \frac{At^2 + Bt}{C + t} \] The dimension of \( A \), \( B \), and \( C \) is:
- JEE Main - 2025
- Physics
- Dimensional Analysis
- The pair of physical quantities not having the same dimensions is:
- JEE Main - 2025
- Physics
- Dimensional Analysis
- Acceleration due to gravity on the surface of earth is \( g \). If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________________ g.
- JEE Main - 2025
- Physics
- Dimensional Analysis
Questions Asked in NEET exam
- Given below are two statements :
Statement I : In the nephron, the descending limb of loop of Henle is impermeable to water and permeable to electrolytes.
Statement II : The proximal convoluted tubule is lined by simple columnar brush border epithelium and increases the surface area for reabsorption.
In the light of the above statements, choose the correct answer from the option given below :- NEET (UG) - 2024
- Nephrons
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The potential (V) at any axial point, at 2 m distance(r) from the centre of the dipole of dipole moment vector\(\vec{P}\) of magnitude, 4 × 10-6 C m, is ± 9 × 103 V.
(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)
Reason R : \(V=±\frac{2P}{4\pi \epsilon_0r^2}\), where r is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below :- NEET (UG) - 2024
- Magnetic Field
- \(^{290}_{82}X\stackrel{\alpha}{\rightarrow}Y\stackrel{e^+}{\rightarrow}Z\stackrel{\beta^-}{\rightarrow}P\stackrel{e^-}{\rightarrow}Q\)
In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are :- NEET (UG) - 2024
- Nuclear physics
- In an ecosystem if the Net Primary Productivity (NPP) of first trophic level is 100x (kcal m-2)yr-1, what would be the GPP (Gross Primary Productivity) of the third trophic level of the same ecosystem?
- NEET (UG) - 2024
- Ecosystems
The output (Y) of the given logic gate is similar to the output of an/a :
- NEET (UG) - 2024
- Digital Electronics and Logic Gates
Concepts Used:
Dimensional Analysis
Dimensional Analysis is a process which helps verify any formula by the using the principle of homogeneity. Basically dimensions of each term of a dimensional equation on both sides should be the same.
Limitation of Dimensional Analysis: Dimensional analysis does not check for the correctness of value of constants in an equation.
Using Dimensional Analysis to check the correctness of the equation
Let us understand this with an example:
Suppose we don’t know the correct formula relation between speed, distance and time,
We don’t know whether
(i) Speed = Distance/Time is correct or
(ii) Speed =Time/Distance.
Now, we can use dimensional analysis to check whether this equation is correct or not.
By reducing both sides of the equation in its fundamental units form, we get
(i) [L][T]-¹ = [L] / [T] (Right)
(ii) [L][T]-¹ = [T] / [L] (Wrong)
From the above example it is evident that the dimensional formula establishes the correctness of an equation.