WB JEE 2023 | Units & Measurements Question 9 | Physics

A modified gravitational potential is given by $$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{r}}+\frac{\mathrm{A}}{\mathrm{r}^{2}}$$. If the constant A is expressed in terms of gravitational constant (G), mass (M) and velocity of light (c), then from dimensional analysis, A is,

$$\frac{G^{2} M^{2}}{c^{2}}$$

$$\frac{\mathrm{GM}}{\mathrm{c}^{2}}$$

$$\frac{1}{c^{2}}$$

Dimensionless

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative error in $$Z = {{{A^4}{B^{{1 \over 3}}}} \over {C{D^{{3 \over 2}}}}}$$ is

$${{127} \over 2}\% $$

$${{127} \over 5}\% $$

$${{127} \over 6}\% $$

$${{127} \over 7}\% $$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where k_B is the Boltzmann constant and A is the area of the black hole. The $$\beta$$ has dimension of

L²

ML²L^$$-$$1

L^$$-$$2

dimensionless

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck constant (h) as [consider $${1 \over {4\pi {\varepsilon _0}}} \equiv 1$$ unit]

$${{{h^2}} \over {m{e^2}}}$$

$${{m{e^4}} \over {{h^2}}}$$

$${{{m^2}{e^4}} \over {{h^2}}}$$

$${{m{e^2}} \over {{h^2}}}$$

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