Acceleration Due to Gravity of the Earth

Gravitational force on point mass in side solid sphere.

(i) When a point mass $m$ is considered at distance $r$ from the centre of solid sphere inside it then gravitational force on point mass is proportional to.

An object of mass $100 \mathrm{kg}$ is sent inside the earth radially for a distance of $300 \mathrm{km}$, What is the gravitational force of attraction between the object and the earth? (Take radius of the earth $R_e = 6371 \mathrm{km}$, Mass of the earth $M_e = 5.97\times {10}^{24} \mathrm{kg}$.)

The force of attraction due to a solid sphere of uniform density, on a point mass situated inside it is zero.

Derive an expression for the gravitational force of a point mass $m$ kept inside a solid sphere of mass $M$ and radius $R$ at a distance of $r$ from the center of the sphere.

The ratio of the SI unit to CGS unit of acceleration is

Assuming the earth to be a homogeneous sphere, determine the density of the earth from following data:

$g=9.8 \mathrm{m}/{\mathrm{s}}^2, G= 6.673 \mathrm{x} {10}^{-11} {\mathrm{Nm}}^2/{\mathrm{kg}}^2, R=6400 \mathrm{km}.$

A body weighs $3.5 \mathrm{kgwt}$ on the surface of the earth. What will be its weight on the surface of a planet whose mass is $\frac{1}{7}\mathrm{th}$ of the mass of the earth and radius half of that of the earth ?

The acceleration due to gravity on the earth's surface is 

The value of acceleration due to gravity is maximum at ____.

A body falling freely under gravity passes through two points $30\mathrm{ }\mathrm{m}$ apart in $1 \mathrm{s}$. From what distance above the upper point it began to fall? $(\text{Take}\mathrm{ }g=9.8\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2})$

As astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of $100\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$. What is the acceleration of the astronaut the instant he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him)

Assertion: In a free fall, weight of a body becomes effectively zero.

Reason: Acceleration due to gravity acting on a body having free fall is zero.

The acceleration due to gravity '$g$' and mean density of the earth $\rho$ are related by which of the following relations?

(Where, $G$ is the gravitational constant and $R$ is radius of earth.)

Acceleration due to gravity at earth's surface is $10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$. The value of acceleration due to gravity at the surface of a planet of mass one fifth and radius $\frac{1}{2}$ of the earth is:

If the diameter of mars is $6760 \mathrm{km}$ and mass is one-tenth of the earth. The diameter of earth is $12742 \mathrm{km}$. If acceleration due to gravity on earth is $9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, the acceleration due to gravity on mars is

An object weighs $10 N$ at the north-pole of the earth. In a geostationary satellite distance $7R$ from the centre of earth (of radius $R$) what will be its true weight?

If the radius of the earth were to shrink by $1\%$ its mass remaining same, the acceleration due to gravity on the earth's surface would

If the radius of the Earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the Earth's surface would

Three weights $w,2w \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }3w$ are connected to identical spring suspended from a rigid horizontal rod. The assembly of the rod and weights fall freely. The positions of the weight from the rod are such that

Earth binds the atmosphere because of