Question

A quantity $f$ is given by $f=\sqrt{\frac{h{c}^5}{G}}$ where $c$ is speed of light, $G$ univasal gravitational constant and $h$ is the Planck’s constant. Dimension of $f$ is that of:

JEE Main 2020 (09 Jan Shift 1)

Options

• A: area
• B: energy
• C: momentum
• D: volume

Question

Match List I with List II.

Choose the correct answer from the options given below

JEE Main 2021 (27 Jul Shift 2)

Options

• A: $(\mathrm{a}) \to (\mathrm{iii}),\; (\mathrm{b}) \to \left(\mathrm{ii}\right),\left(\mathrm{c}\right)\to \left(\mathrm{iv}\right),\left(\mathrm{d}\right)\to \left(\mathrm{i}\right)$
• B: $(\mathrm{a}) \to (\mathrm{iii}),\; (\mathrm{b}) \to (\mathrm{iv}),\; (\mathrm{c}) \to (\mathrm{ii}),\; (\mathrm{d}) \to \left(\mathrm{i}\right)$
• C: $(\mathrm{a}) \to (\mathrm{iv}),\; (\mathrm{b}) \to (\mathrm{ii}),\; (\mathrm{c}) \to (\mathrm{iii}),\; (\mathrm{d}) \to \left(\mathrm{i}\right)$
• D: $(\mathrm{a}) \to (\mathrm{iv}),\; (\mathrm{b}) \to (\mathrm{iii}),\; (\mathrm{c}) \to (\mathrm{ii}),\; (\mathrm{d}) \to \left(\mathrm{i}\right)$

Question

Given below are two statements:

Statement (I) : Planck's constant and angular momentum have the same dimensions.

Statement (II) : Linear momentum and moment of force have the same dimensions.

In light of the above statements, choose the correct answer from the options given below :

JEE Main 2024 (27 Jan Shift 1)

Options

• A: Statement I is true but Statement II is false
• B: Both Statement I and Statement II are false
• C: Both Statement I and Statement II are true
• D: Statement I is false but Statement II is true

Question

If momentum $\left[P\right]$, area $\left[A\right]$ and time $\left[T\right]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is

JEE Main 2022 (25 Jul Shift 1)

Options

• A: $\left[{\mathrm{PA}}^{-1}{\mathrm{T}}^0\right]$
• B: $\left[{\mathrm{PAT}}^{-1}\right]$
• C: $\left[{\mathrm{PA}}^{-1}\mathrm{T}\right]$
• D: $\left[{\mathrm{PA}}^{-1}{\mathrm{T}}^{-1}\right]$

Question

Match List - I with List - II :

Choose the most appropriate answer from the options given below :

JEE Main 2021 (26 Aug Shift 2)

Options

• A: $\left(\mathrm{a}\right)-\left(\mathrm{iii}\right), \left(\mathrm{b}\right)-\left(\mathrm{ii}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{i}\right)$
• B: $\left(\mathrm{a}\right)-\left(\mathrm{iii}\right), \left(\mathrm{b}\right)-\left(\mathrm{i}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{ii}\right)$
• C: $\left(\mathrm{a}\right)-\left(\mathrm{ii}\right), \left(\mathrm{b}\right)-\left(\mathrm{iv}\right), \left(\mathrm{c}\right)-\left(\mathrm{i}\right), \left(\mathrm{d}\right)-\left(\mathrm{iii}\right)$
• D: $\left(\mathrm{a}\right)-\left(\mathrm{ii}\right), \left(\mathrm{b}\right)-\left(\mathrm{i}\right), \left(\mathrm{c}\right)-\left(\mathrm{iv}\right), \left(\mathrm{d}\right)-\left(\mathrm{iii}\right)$

Question

A quantity $x$ is given by $(1F{v}^2/W{L}^4 )$ 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 :

JEE Main 2020 (04 Sep Shift 2)

Options

• A: planck's constant
• B: force constant
• C: energy density
• D: coefficient of viscosity

Question

Match List-I with List-II. 

$\begin{array}{|clcl|}\hline & \text{ List-I }& & \text{ List-II }\\ \text{ A. }& \text{ Coefficient of viscosity }& \text{ I. }& \left[{\mathrm{ML}}^2 {\mathrm{T}}^{-2}\right]\\ \text{ B. }& \text{ Surface Tension }& \text{ II. }& \left[{\mathrm{ML}}^2 {\mathrm{T}}^{-1}\right]\\ \text{ C. }& \text{ Angular momentum }& \text{ III. }& \left[{\mathrm{ML}}^{-1} {\mathrm{T}}^{-1}\right]\\ \text{ D. }& \text{ Rotational kinetic energy }& \text{ IV. }& \left[{\mathrm{ML}}^0 {\mathrm{T}}^{-2}\right]\\ \hline\end{array}$

JEE Main 2024 (30 Jan Shift 1)

Options

• 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

The dimension of stopping potential $V_0$ in photoelectric effect in units of Planck’s constant ‘ $h$ ’, speed of light ‘ $c$ ’ and Gravitational constant ‘ $G$ ’ and ampere $A$ is:

JEE Main 2020 (08 Jan Shift 1)

Options

• A: $h^{\frac{1}{3}}{G}^{\frac{2}{3}}{c}^{\frac{1}{3}}{A}^{-1}$
• B: $h^0{c}^5{G}^{-1}{A}^{-1}$
• C: $h^{-\frac{2}{3}}{c}^{-\frac{1}{3}}{G}^{\frac{4}{3}}{A}^{-1}$
• D: $h^2{G}^{\frac{3}{2}}{c}^{\frac{1}{3}}{A}^{-1}$

Question

An expression of energy density is given by $u=\frac{\alpha }{\beta }\sin \left(\frac{\alpha x}{kt}\right)$, where $\alpha , \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be

JEE Main 2022 (27 Jul Shift 2)

Options

• A: $\left[{\mathrm{ML}}^2{ \mathrm{T}}^{-2}{\theta }^{-1}\right]$
• B: $\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$
• C: $\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\right]$
• D: $\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^0\right]$

Question

If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{\mathrm{uG}}$ :

JEE Main 2024 (05 Apr Shift 1)

Options

• A: pressure gradient per unit mass
• B: Gravitational potential
• C: Energy per unit mass
• D: Force per unit mass

Question

The equation of stationary wave is : $y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. }$ Which of the following is NOT correct :

JEE Main 2024 (04 Apr Shift 1)

Options

• A: The dimensions of $n / \lambda$ is [T]
• B: The dimensions of $\mathrm{n}$ is $\left[\mathrm{LT}^{-1}\right]$
• C: The dimensions of $x$ is [L]
• D: The dimensions of $\mathrm{nt}$ is [L]