Two planets have the same average density but different radii. The larger planet has twice the radius of the smaller planet. What is the ratio of the gravitational field strength on the surface of the larger planet to that on the surface of the smaller planet?

If the earth stops rotating, the value of $g$ at the equator

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 ${m}$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

If the gravitational field intensity at a specific location is 50 N/kg, what gravitational force would a 0.24 kg object experience at that location?

$n$-point masses each of mass $m$ are placed at each corner of a regular polygon of edge langth $l$. The distance between vertex and the centre of polygon is $r$. The gravitational potential at the centre of the polygon is

At what height from the ground will the value of '$g$' be the same as that in $10\;km$ deep mine below the surface of earth

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then

The gravitational field in a region is given by $\vec{E}=\left(5 \mathrm{~N} \mathrm{~kg}^{-1}\right) \vec{i}+\left(12 \mathrm{~N} \mathrm{~kg}^{-1}\right) \vec{j}$. Find the potential at the points $(12 \mathrm{~m}, 0)$ and $(0,5 \mathrm{~m})$ if the potential at the origin is taken to be zero.

A uniform ring of mass $m$ and radius $a$ is placed directly above a uniform sphere of mass $M$ and of equal radius. The centre of the ring is at a distance $\sqrt{3} a$ from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

Two astronauts have deserted their space ships in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to one another. How long will it be before the gravitational attraction brings them 1 cm closer together?

A test particle is moving in a circular orbit in the gravitational field produced by mass density $\rho (r) = \frac{K}{{{r^2}}}$. Identify the correct relation between the radius R of the particle’s orbit and its period T