JEE Main 2024 (Online) 4th April Evening Shift | Gravitation Question 12 | Physics

A metal wire of uniform mass density having length $$L$$ and mass $$M$$ is bent to form a semicircular arc and a particle of mass $$\mathrm{m}$$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :

$$\frac{\mathrm{GmM} \pi^2}{\mathrm{~L}^2}$$

$$\frac{\mathrm{GMm} \pi}{2 \mathrm{~L}^2}$$

$$\frac{2 \mathrm{GmM} \pi}{\mathrm{L}^2}$$

JEE Main 2024 (Online) 1st February Evening Shift

MCQ (Single Correct Answer)

-1

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, :

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

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

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

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

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