AIEEE 2005 | Gravitation Question 199 | Physics

A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm.$$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $$G$$ $$ = 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}$$)

$$3.33 \times {10^{ - 10}}\,J$$

$$13.34 \times {10^{ - 10}}\,J$$

$$6.67 \times {10^{ - 10}}\,J$$

$$6.67 \times {10^{ - 9}}\,J$$

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

$${1 \over 4}mgR$$

$$2mgR$$

$${1 \over 2}mgR$$

$$mgR$$

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

The time period of an earth satellite in circular orbit is independent of

both the mass and radius of the orbit

radius of its orbit

the mass of the satellite

neither the mass of the satellite nor the radius of its orbit