JEE Main 2024 (Online) 1st February Evening Shift | Gravitation Question 37 | Physics

A light planet is revolving around a massive star in a circular orbit of radius $\mathrm{R}$ with a period of revolution T. If the force of attraction between planet and star is proportional to $\mathrm{R}^{-3 / 2}$ then choose the correct option :

$\mathrm{T}^2 \propto \mathrm{R}^{7 / 2}$

$\mathrm{T}^2 \propto \mathrm{R}^3$

$\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}$

$\mathrm{T}^2 \propto \mathrm{R}^{3 / 2}$

JEE Main 2024 (Online) 1st February Morning Shift

MCQ (Single Correct Answer)

-1

If $\mathrm{R}$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2 \mathrm{~m} / \mathrm{s}^2$, then the length of the second's pendulum at a height $\mathrm{h}=2 R$ from the surface of earth will be, :

$\frac{1}{9} \mathrm{~m}$

$\frac{8}{9} \mathrm{~m}$

$\frac{2}{9} \mathrm{~m}$

$\frac{4}{9} \mathrm{~m}$

JEE Main 2024 (Online) 31st January Evening Shift

MCQ (Single Correct Answer)

-1

The mass of the moon is $$\frac{1}{144}$$ times the mass of a planet and its diameter is $$\frac{1}{16}$$ times the diameter of a planet. If the escape velocity on the planet is $$v$$, the escape velocity on the moon will be :

$$\frac{\mathrm{v}}{4}$$

$$\frac{\mathrm{v}}{6}$$

$$\frac{\mathrm{V}}{12}$$

$$\frac{\mathrm{v}}{3}$$

JEE Main 2024 (Online) 31st January Morning Shift

MCQ (Single Correct Answer)

-1

Four identical particles of mass $$m$$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $$\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{L^2}$$, the length of the sides of the square is