Consider a planet in some solar system which has a mass double the mass of Earth and density equal to the average density of Earth. If the weight of an object on Earth is $W$,then the weight of the same object on that planet will be

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

The value of acceleration due to gravity at Earth's surface is $9.8\, m\,s^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\, m\,s^{-2}$,is close to: (Radius of Earth $= 6.4 \times 10^6\, m$)

The mass of a spherical planet is $4$ times the mass of the earth, but its radius $(R)$ is the same as that of the earth. How much work is done in lifting a body of mass $5 \,kg$ through a distance of $2 \,m$ on the planet (in $\,J$)? (Take $g = 10 \,ms^{-2}$ for Earth)

At what depth below the surface of the earth,will the acceleration due to gravity $g$ be half of its value at $1600 \, km$ above the surface of the earth?

Obtain an expression for the acceleration due to gravity of the Earth at a depth $d$ below its surface.