1
AIPMT 2011 Prelims
+4
-1
A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If $$v$$1 and $$v$$2 are the linear velocities at these points respectively, then the ratio $${{{v_1}} \over {{v_2}}}$$ is
A
(r1 /r2)2
B
r2/r1
C
(r2/r1)2
D
r1/r2
2
AIPMT 2010 Mains
+4
-1
The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below

The correct figure is
A
(4)
B
(1)
C
(2)
D
(3)
3
AIPMT 2010 Mains
+4
-1
(1)   Centre of gravity (C.G) of a body is the point at which the weight of the body acts
(2)   Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
(3)   To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.
(4)   The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis.

Which one of the following pairs of statements is correct ?
A
(4) and (1)
B
(1) and (2)
C
(2) and (3)
D
(3) and (4)
4
AIPMT 2010 Mains
+4
-1
The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R1 to another of radius R2(R2 > R1) is
A
GmM $$\left( {{1 \over {R_1^2}} - {1 \over {R_2^2}}} \right)$$
B
GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
C
2GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
D
$${1 \over 2}$$GmM $$\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$
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