AIEEE 2005 | Gravitation Question 176 | Physics

The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$d$$ below the surface of earth. When both $$d$$ and $$h$$ are much smaller than the radius of earth, then which one of the following is correct?

$$d = {{3h} \over 2}$$

$$d = {h \over 2}$$

$$d = h$$

$$d = 2\,h$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

$${{g{R^2}} \over {R + x}}$$

$${{gR} \over {R - x}}$$

$${gx}$$

$${\left( {{{g{R^2}} \over {R + x}}} \right)^{1/2}}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius $$R$$ around the sun will be proportional to

$${R^n}$$

$${R^{\left( {{{n - 1} \over 2}} \right)}}$$

$${R^{\left( {{{n + 1} \over 2}} \right)}}$$

$${R^{\left( {{{n - 2} \over 2}} \right)}}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass $$m$$ raised from the surface of the earth to a height equal to the radius $$R$$ of the earth is

$${1 \over 4}mgR$$

$$2mgR$$

$${1 \over 2}mgR$$

$$mgR$$

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