Application of Dimensional analysis (IV)- To find the unit of physical quantity in a given system" – JEE Main Study Material

Question

CGS unit of Force is

A.	$kg m s^{-2}$
B.	Newton
C.	$kg m s$
D.	gram-centimeter/second²

Question

Asked in: JEE Main 2020-2020

The quantities $x = \frac{1}{\sqrt{\mu_o\epsilon_o}}, y = \frac{E}{B}$ $z = \frac{l}{CR}$ are defined where C - capacitance, R - resistance, l - length, E - Electric field, B - magnetic field $\epsilon_o \mu_o$ - free space permittivity and permeability respectively, then:

A.	only y and z have same dimension
B.	only x and z have same dimension
C.	only x and y have same dimension
D.	x, y, and z have same dimension

Question

Asked in: JEE Main 2020-2020

A quantity x is given by $(IFv^{2}/WL^{4})$ in terms of a moment of inertia I, force F, velocity v, work W and length L. The dimensional formula for the x is the same as that of:

A.	planck's constant
B.	force constant
C.	Energy density
D.	coefficient of viscosity

Question

Asked in: JEE Main 2022-2022

Match List I with List II.

List-I	List-II
A. Torque	I. $\mathrm{ \mathrm{Nms}^{-1} }$
B. Stress	II. $\mathrm{ \mathrm{J} \mathrm{kg}^{-1}}$
C. Latent Heat	III. $\mathrm{ Nm }$
D. Power	IV. $\mathrm{\mathrm{Nm}^{-2}}$

Choose the correct answer from the options given below:

A.	A-III, B-II, C-I, D-IV
B.	A-III, B-IV, C-II, D-I
C.	A-IV, B-I, C-III, D-II
D.	A-II, B-III, C-I, D-IV

Question

Asked in: JEE Main 2021-2021

If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

A.	$\left[\mathrm{FVT}^{-1}\right]$
B.	$\left[\mathrm{FTV}^{-1}\right]$
C.	$\left[\mathrm{FT}^2 \mathrm{~V}\right]$
D.	$\left[\mathrm{FT}^{-1} \mathrm{~V}^{-1}\right]$

Question

Asked in: JEE Main 2021-2021

In a typical combustion engine the workdone by a gas molecule is given by $W=\alpha ^{2}\beta e\frac{-Bx^{2}}{kT}$ where x is the displacement, k is the Boltzmann constant and T is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be :

A.	$\left [ M^{2} L\; T^{-2}\right ]$
B.	$\left [ M\; L\; T^{-1}\right ]$
C.	$\left [ M^{0}\; L\; T^{0}\right ]$
D.	$\left [ M\; L\; T^{-2}\right ]$

Question

Asked in: JEE Main-2024

The truth table of the given circuit diagram is:

A.	A B Y 0 0 1 0 1 0 1 0 0 1 1 1
B.	A B Y 0 0 0 0 1 1 1 0 1 1 1 0
C.	A B Y 0 0 0 0 1 0 1 0 0 1 1 1
D.	A B Y 0 0 1 0 1 1 1 0 1 1 1 0

Question

Asked in: JEE Main-2024

Match List - I with List - II.

List – I	List – II
(A) Coefficient of viscosity	(I) $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$
(B) Surface tension	(II) $\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right]$
(C) Angular momentum	(III) $\left[\mathrm{M} \mathrm{L}^{-1} \mathrm{~T}^{-1}\right]$
(D) Rotational kinetic energy	(IV) $\left[\mathrm{M} \mathrm{L}^0 \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below :

A.	(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
B.	(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
C.	(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
D.	(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Question

One Newton is equal to -

A.	10⁷ dyne
B.	10³ dyne
C.	10⁵ dyne
D.	10² dyne

Question

The unit of work is -

A.	kg-m/sec
B.	kg-m²/sec²
C.	kg-m²/sec
D.	kg-m-sec

Question

Asked in: JEE Main-2024

What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning?

A.	$\left[\mathrm{M}^0 \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
B.	$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
C.	$\left[\mathrm{M}^{-1} \mathrm{~L}^5 \mathrm{~T}^3\right]$
D.	$\left[\mathrm{M}^6 \mathrm{~L}^7 \mathrm{~T}^4\right]$

Exam	Chapter
JEE MAIN	Physics and Measurement

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Application of Dimensional analysis (IV)- To find the unit of physical quantity in a given system" - (Concept)

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