Variation in Acceleration due to Gravity

A (nonrotating) star collapses onto itself from an initial radius ${\text{R}}_{\text{i}}$ with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration ${\text{a}}_{\text{g}}$ on the surface of the star as a function of the radius of the star during the collapse?

If a tunnel is cut at any orientation through the earth, then a ball released from one end will reach the other end in how much time (neglect earth rotation)? 

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $V$. Due to the rotation of the planet about its axis the acceleration due to gravity $g$ at equator is $\frac{1}{2}$ of $g$ at poles. The escape velocity of a particle on the planet in terms of $V$ from the pole of the planet is,

The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of a pendulum on this planet if it is a second pendulum on earth?

If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g same?

What happens to the acceleration due to gravity with the increase in altitude from the surface of the earth?

Acceleration due to gravity at a height of $h$ is $25\%$ of that at the surface of the Earth. The value of $h$ in terms of radius of earth $R$ is
radius of the Earth. 

The mass of body on surface of the earth is $100 \mathrm{kg}$. What will be its (i) mass and (ii) weight at an altitude of $1000 \mathrm{km}$?

$(R=6400 \mathrm{km}, g=9.8 \mathrm{m}/{\mathrm{s}}^2)$

Discuss the variation of $\mathrm{g}$ with latitude.

Discuss the variation of $\mathrm{g}$ with depth.

Discuss the variation of $\mathrm{g}$ with altitude.

What is acceleration due to gravity at the surface of mars if its diameter is $6760 \mathrm{km}$ and mass one tength that of earth. The diameter of earth is $12742 \mathrm{km}$ and acceleration due to gravity on earth is $9.8 \mathrm{m}/{\sec }^2$ 
 

What is the depth from the surface of the earth at which the acceleration due to gravity is $25\%$ of the acceleration due to gravity at the surface?

Find the percentage decrease in weight of a body, when taken $16 \mathrm{k}\mathrm{m}$ below the surface of the earth. Take radius of the earth as $\mathrm{6,400} \mathrm{k}\mathrm{m}$.

A body weighs $64 \mathrm{N}$ on the surface of the earth. What is the gravitational force (in $\mathrm{N}$) on it due to the earth at a height equal to one-third of the radius of the earth?

Weight of body at the centre of the earth is _____.

Which of the following statements are true about acceleration due to gravity?

$R$ is the radius of Earth and $\omega$ is its angular velocity and $g_p$ is the value of $g$ at the poles. The effective value of $g$ at a latitude $\lambda ={60}^o.$

The reading of a spring balance corresponds to $\text{100 N}$ while situated at the north pole and a body is kept on it. The weight record on the same scale if is shifted to the equator, is  ( take, $\mathrm{g}=10\mathrm{ }{\mathrm{ms}}^{-2}$ and radius of the earth, $\mathrm{R}=6.4\times {10}^6\mathrm{ }\mathrm{m}$ )

At what height from the surface of earth the gravitation potential and the value of g are $-5.4\times {10}^7\mathrm{J}\mathrm{ }\mathrm{k}{\mathrm{g}}^{-2}$ and $6.0\mathrm{ }\mathrm{m}{\mathrm{s}}^{-2}$ respectively? Take the radius of earth as$6400 \mathrm{km}$: