Acceleration Due to Gravity of the Earth

Let $\omega$ be the angular velocity of the earth's rotation about its axis. Assume that the acceleration due to gravity on the earth's surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth $\mathrm{d}$ below earth's surface at a pole $\left(d\ll R\right)$. The value of $d$ is:

Two satellites $P$ and $Q$ are moving in different circular orbits around the Earth(radius $R$). The heights of $P$ and $Q$ from the Earth surface are $h_P$ and $h_Q$, respectively, where $h_P=\frac{R}{3}$. The accelerations of $P$ and $Q$ due to Earth’s gravity are $g_P$ and $g_Q$, respectively. If $\frac{g_P}{g_Q}=\frac{36}{25}$, what is the value of $h_Q$?

A mass is attached to a spring that hangs vertically. The extension produced in the spring is $6 \mathrm{cm}$ on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be :

Which one of the following statements is true?

Two planets A and B of radii $R$ and $1.5 R$ have densities $\rho$ and $\frac{\rho }{2}$ respectively. The ratio of acceleration due to gravity at the surface of B to A is:

The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\frac{\rho }{3}$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A:g_B\right)$ will be
 

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing $W$ on earth will weigh on that planet:

Which of the following expression gives the value of acceleration due to gravity $g^{\text{'}}$ at the altitude $h$ above the surface of Earth.

($R=$radius of Earth, $g=$acceleration due to gravity at surface of Earth)

On a planet $\rho$(mass density) is same as that of Earth while mass of planet is twice than that of Earth. Ratio of weight of a body on surface of the planet to that on Earth is equal to:

At what height above the Earth's surface does the value of $g$ becomes $36\%$ of the value at the surface of Earth?

If $g_1$ and $g_2$ denote acceleration due to gravity on the surface of the earth and on a planet whose mass and radius is thrice that of earth, then

Find the weight of an object on Jupiter if its weight on earth is $980 \mathrm{N}$.

Mass of Jupiter, $M_J=1.9\times {10}^{27} \mathrm{kg}$

Radius of Jupiter, $R_J=7.1\times {10}^7 \mathrm{m}$

What is interplanetary space where value of $\mathrm{g}=0$ ?

There are two spherical planets $A$ and $B$. The density of $A$ and $B$ are same but radius of $A$ is three times that of $B$. Then ratio of acceleration due to gravity on the surfaces of $A$ and $B$ i.e., $\frac{g_A}{g_B}$ is

An object is dropped from a height onto the floor. Which one of the following remains uniform as it falls?

Consider a body that has a mass double the mass of earth and $3$ times the radius of the earth and the acceleration due to the gravity of the earth is $g$. Find the acceleration due to the gravity of the body?

Find the gravitational force between Earth and $1 kg$the object.

An empty plastic box of mass $\mathrm{m}$ is found to accelerate up at a rate of $\frac{g}{6}$ when placed deep inside water. Then the mass of sand be filled in it so that it may accelerate down at a rate of $\frac{g}{6}$ is

Determine the average density of the planet for which the length of day is $6 \mathrm{hrs}$. When we weigh a body using spring balance at its equator, the scale shows weight $10\%$ less weight than that at the pole. Fill $\frac{\rho }{{10}^4}$ in $\mathrm{kg} {\mathrm{m}}^{-3}$ in OMR sheet.

What is the gravitational field on a point mass kept inside a soild sphere?