1
AIEEE 2005
+4
-1
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 $$G$$ $$= 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}$$)
A
$$3.33 \times {10^{ - 10}}\,J$$
B
$$13.34 \times {10^{ - 10}}\,J$$
C
$$6.67 \times {10^{ - 10}}\,J$$
D
$$6.67 \times {10^{ - 9}}\,J$$
2
AIEEE 2005
+4
-1
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?
A
$$d = {{3h} \over 2}$$
B
$$d = {h \over 2}$$
C
$$d = h$$
D
$$d = 2\,h$$
3
AIEEE 2005
+4
-1
Average density of the earth
A
is a complex function of $$g$$
B
does not depend on $$g$$
C
is inversely proportional to $$g$$
D
is directly proportional to $$g$$
4
AIEEE 2004
+4
-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
A
$${{g{R^2}} \over {R + x}}$$
B
$${{gR} \over {R - x}}$$
C
$${gx}$$
D
$${\left( {{{g{R^2}} \over {R + x}}} \right)^{1/2}}$$
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