1
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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 :
A
$\mathrm{T}^2 \propto \mathrm{R}^{7 / 2}$
B
$\mathrm{T}^2 \propto \mathrm{R}^3$
C
$\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}$
D
$\mathrm{T}^2 \propto \mathrm{R}^{3 / 2}$
2
JEE Main 2024 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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, :
A
$\frac{1}{9} \mathrm{~m}$
B
$\frac{8}{9} \mathrm{~m}$
C
$\frac{2}{9} \mathrm{~m}$
D
$\frac{4}{9} \mathrm{~m}$
3
JEE Main 2024 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
$$\frac{\mathrm{v}}{4}$$
B
$$\frac{\mathrm{v}}{6}$$
C
$$\frac{\mathrm{V}}{12}$$
D
$$\frac{\mathrm{v}}{3}$$
4
JEE Main 2024 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
4L
B
3L
C
2L
D
$$\frac{L}{2}$$
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